subtending the distance of those two places Taking therefore the length of GE with the Compasses and setting one foote in H where the degrees begin the other stretched forwards in the circle will point you out the distance of Saint Thomas Iland and London 52 degrees of a great circle and about one halfe that is 1050 leagues or 3150 English miles If both places have Latitude do the like for both places as before you did for the one place having Latitude till you have crossed both diameters with perpendiculars then take with your Compasses the distance of those crossings Now if both their Latitudes be of one denomination that is both Northerly or both Southerly and equal set one foote of the Compasses where the degrees begin to be numbred in the circle and the other foote extended therein that way which the numbers succeede will shew you the distance As for example London and Cape Blanco neere the coast of New-found land have both Northerly and almost equal Latitudes of 51 degrees 32 minutes Having therefore drawn as well the diameters BC and DL from B determining the Longitude of London viz. 22 degrees and from the point of the Longitude of Cape Blanco which admit to be 331 degrees as also the perpendiculars or sines of both their Latitudes EF and KL as before was shewed crossing the diameters in F and L the distance FL taken with the Compasses and translated into the circle as in the former example will shew you the distance of Cape Blanco from London to be almost 31 degrees of a great circle that is 620 leagues or 1860 miles If the Latitudes be not both equal and also of one denomination leaving one foote of the Compasses in the crossing of the sine or perpendicular descending from the point of the greater Latitude with the other foote make a pricke in the same diameter wherein that crossing is then if the Latitudes be both of one denomination â—ake with the Compasses the length of the perpendicular or sine drawn from the point of the lesser Latitude and setting one foote in the point of the greater Latitude with the other make a prick in the perpendicular descending from it that is in the sine thereof Take the distance of this pricke from the former made in the diameter This distance transferred into the circle as in the first example will give you the distance of the places given As London and Hierusalem have both Northerly and unequal Latitudes Hierusalems Latitude being onely 32 degrees First therefore note in the circle both their Longitudes the Longitude of London viz. 22 degrees as before with B The Longitude of Hierusalem 68 degrees note with M Let the perpendicular or the sines of the Latitudes of London and Hierusalem EF and NO be drawn as in the former examples Make FP equal to OF and PQ equal to NO The space betwixt P and Q taken with the Compasses and then both feet set in the circle in such sort as in the first example was shewed shall containe between them the desired distance of Hierusalem from London 38 degrees and about ¾ that is 775 leagues which are 2325 miles But if the Latitudes be of divers denominations that is one Northerly and the other Southerly continue forth the perpendicular that crosseth the diameter wherein the foresaid prick was made till it be equal to both perpendiculars that is to the sines of both Latitudes The distance of the end of this continued perpendicular from the pricke aforesaid in the diameter taken with the Compasses and translated into the graduated peripherie of the circle as before will shew you how many degrees of a great circle are contained between both places To shut up this matter with one example suppose you would know how farre Cusco in Peru is from London Let the Longitude of Cusco be 295 degrees the Latitude 11 degrees Southerly The Longitude of London as before 22 degrees the Latitude 51 degrees 32 minutes From both these Longitudes noted in the circle with B and R draw the diameters as before BC and RV as also the perpendiculars or sines of their Latitudes EF and T S Make FX equal to FS the distance of those sines and EY equal to ST the sine of Cuscoes Latitude Take the distance XY between the feet of the Compasses and set them both in the circumference of the circle as in the first example so shall you find that there are betwixt London and Cusco almost 97 degrees of a great circle that is 1940 leagues or 5820 miles If you had rather keepe within the compasse of the circle make the perpendicular XZ equal to ST and proceede with EZ as you did before with XY Paste this upon the Margin of Letter N. fol. 65. so as it may ly open all the while the fore-going matter of the same Chap. is reading Also because all the sines of Latitude being perpendicular to the same plain of the Aequinoctial are Parallels by the 5. e 21. Ram. 6. pr. 11. Eucl. Therefore by the 11. e 2. Ram. or 35. d. 1. Eucl. FL is the line subtending the distance of London and Cape â—â—anco Again because FP whereto EF is perpendicular is made equal to FO the distance of the sines of London and Hierusalem to which distance EF is also perpendicular in the Globe and EQ also equal to NO Therefore FQ being the difference 〈◊〉 the sines of Londons and Hierusalems Latitudes there must needs be the same distance betwixt P and Q that there is between the tops of the sines of Hierusalems and Londons Latitudes in the Globe Lastly FX being equal to FS the distance of the sines of Latitude of London and Cusco in Peru and XZ perpendicular to FX and equal to ST the sine of Cuscoes Latitude as EF is the sine of Londons Latitude and perpendicular to the same line XF EZ to which XY is equal by the 6. c. 12. e 5 Ram. 33. pr. 1. Eucl. YE being equal and Parallel to XZ must needs be equal to a streight line extended within the Globe between the points of Latitude of Cusco and London Now out of this demonstration it were an easie matter if any list take the pains to be so curious to find out the distance of any two places Arithmetically by the doctrine of Triangles having alwaies two sides given which are the sines of the complements of the Latitudes of the two places as OP FP LP FP RP FP AP FP together with the angle contained between them that is the difference of their Longitudes whereby FA FO FL FS the distances of the sines of Latitude being found by 〈◊〉 2 3 4 5 Copernic de Triang planis the lines also subtending the distances of the places may most easily be found by the 3. Copernic de Triang plan For the squares of the distance of the sines and of the difference of the sines of their Latitudes if both be Northerly or both Southerly or of the sum of 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
55 160 401.357 537.178 251.865.582  56 160 938.535 545.704 260.459.920 8.594.338 57 161 484.239 554.505 271 919.077 11.459.157 58 162 038 744 563.594 289 107.811 17.188.734 59 162.602.338 572.986 323.485.279 34.377.468 CHAP. III. The use of the two first columnes of the Table of Latitudes for graduating a Meridian in the general Sea-Chart BEfore you can make use of this Table for the true graduating or dividing of a Meridian of this Chart into his degrees or other parts of Latitude increasing from the Aequinoctial towards the North and South in such proportion as before hath been shewed there must be first some preparation made to that end which may be done after this manner Overthwart the midst of the plain superficies whereupon you will draw the lineaments of the Chart describe a right line representing the Aequinoctial circle which you shall divide into 360 parts or degrees and crosse the same squirewise with right lines by every fift or tenth degree Then take with your compasses the length of half the Aequinoctial that is 180 degrees and setting one foote of your compasses in the mutuall intersection of the Aequinoctial with the perpendicular or Meridian that passeth by either end of the Aequinoctial with the other foote make a prick in the same perpendicular or Meridian the space contained betwixt this prick and the Aequinoctial divide first into three equal parts and every one of these into other three so have you nine in all and againe every one of these into three so have you 27 parts and every one of these parts divide into four so have you 108 parts And againe if there be space enough divide every one of these into 10 or 100. So shall you have 1080 or 10800 parts which will bring you to the Latitude of 85 degrees and something more But if you would make your Chart to any greater Latitude you shall continue forth the foresaid perpendicular and divide it into so many more of the same parts as you shall find needful to attain to the Latitude you desire Then note every fift and tenth part with black lead and set figures at them beginning at the Aequinoctial and from thence proceeding Northwards and Southwards Then look what numbers in the second column are answerable to each degree or minute in the first column of this Table of Latitudes omitting alwaies four or five of the first figures towards the right hand and at the same numbers of parts in the perpendiculars make pricks on either side the Aequinoctial by which pricks draw right lines equidistant from the Aequinoctial for they shall be the Parallels of the true Nautical Planisphere or Sea-Chart Notwithstanding these Parallels are all oâ—â—hem a little further distant from the Aequinoctial then in truth they should be and so much the more the further they are from the Aequinoctial Which error might be something the lesse if the former Table had been first made to smaller parts then minutes But that were a matter more curious then necessarie the Table here before set down being so neere the truth that it is not possible by any rules or Instruments of Navigation to discover any sensible error in the Sea-Chart so farre forth as it shall be made according thereto The figure following containeth onely one part of the Nauticall Planisphaere from the Aequinoctial Northwards because the other part from the Aequinoctial Southwards must be altogether like and equal to this Herein first I drew the Aequinoctial line AC and divided it into 36 equal parts whereof every one is understood to contain ten degrees and I raised perpendiculars from every one of those parts which are the Meridians of the Nauticall Planisphaere every where aequidistant each from other Then I took half the length of the Aequinoctial with the compasses and setting one foot in the end of the Aequinoctial at C with the other foot I made a prick at D in the perpendicular or Meridian CD The space contained betwixt C and D I divided into 1080 parts understanding every one of the smaller parts or segments of the line CD to contain ten lesser parts in such sort as before hath been shewed and set figures to them as here you see for the readier numbring and finding out of any of those parts Then I looked in the former Table what number of equal parts of the Meridian answered to every tenth degree and casting away five of the first figures next the right hand because I conceive the space betwixt C and D to be divided only into 1080 parts I found out the parts answerable to the numbers remaining in the line CD and at those parts I made prickes by which I drew the Parallels As for example in the Table the number answerable to ten degrees is 60 casting away the five first figures towards the right hand therefore I look 60 in the line CD and by that part I draw the Parallel of ten degrees distance from the Aequinoctial Likewise the number answering to twentie degrees omitting the five first figures is 122 therefore by that number of equal parts I draw the parallel of twentie degrees Latitude from the Equinoctial c. And after this manner I drew all the rest as you may see in the former draught The Draught of the Meridians Parallels and Rumbs of the Nautical Planisphear truly made CHAP. IIII. 〈◊〉 way for graduating the Meridian of a general Sea-Chart OTherwise for the dividing of the Meridian of a general Sea-Chart into his degrees and other smaller parts of Latitude when the Chart hath not so great Latitude or breadth from the Equinoctial towards the North or South as hath the figure before set down you may go thus to work First find out what proportion the whole Longitude or lenght of the Chart from West to East must have to the whole breadth thereof betwixt the Parallels of the most Northerly and Southerly places that are to be set down therin which may be done after this manner Out of the second Column of the table of Latitudes take the numbers of equal parts of the Meridian answerable to the greatest North and South Latitudes that are to be set down in the Chart divide those numbers by 600,000 that is the number of equal parts of the Meridian answerable to one degree of the Equinoctial the Quotients will shew how many degrees of the Equinoctial the breadth of the Chart must be on either side the Equinoctial toward the North and South As for example in the generall Sea-â—hart to be adjoyned to this book the Latitude of the North 〈◊〉 of the New land found by the Hollanders about the yeer â—596 and by them called Gebrooken land lying Northwards â—rom Norway is about 80 degrees And the Latitude of Queen Elizabeths Iland first found by Sir Francis Drake lying to the â—outhwards of Magellanes streights is about 53 degrees The â—umbers of equal parts of the Meridian answerable to these Laâ—â—tudes found out in the foresaid Table of
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
after it is touched with the Loadstone by means whereof it seemeth something probable that Seamen may have some help to know their height or Latitude in dark and cloudie weather when neither Sun nor Stars for many daies appear to be observed I thought it should not be impertinent to this place to set down the Theorick that hath been devised of this magnetical inclination together with a demonstration for the making of a Table thereof to every degree of Latitude according to that Theorick to the end that such of our Sea-men as mean to be diligent observers hereof may make heedfull trial of that inclining propertie and compare the same with this Table in all parts of the world where they shall travell especially in those long Voyages to the East and West Indies and in their Northeast or Northwest discoveries The third part may be called Geometrical intreating of the Crosse-staffe and shewing how such errors may be avoided as have been commonly committed in the use thereof either by reason of the parallax or eccentricitie of the eye or by the height of the eye above the water or by the parallax or refraction of the Sun And because for finding the quantitie of the angle that is to be abated out of the apparent altitude of the Sunne or starres observed by this staff for any height of the ey above the water it was needfull to know the quantitie of the earths semidiameter concerning which there is great varietie of opinions amongst learned authors I have therefore in this part of this treatise now shewed divers waies for the more certain finding thereof one of which waies I have also for my more assurance exemplified by observation as meanes and opertunitie served me neere Plimmouth sound anno 1589. The fourth and last part may be called Astronomical wherein my chief intent was to correct the errors that are in the ordinary Tables of declination of the Sunne and fixed starres To which end there is first set down a table of the declination of every minute of the Ecliptick in degrees minutes and seconds calculated for the greatest obliquitie of the Zodiack as it is found by observation in this age 23 degrees 21 minutes and an half Whereto is adjoyned the use thereof for the readie finding of the place of the Sun by his declination given or contrariwise for finding the Suns declination his place being first known After this is shewed the way and means I used for exact observation of the Suns Meridian altitudes with a table of those observations for four yeeres together that so the more certaintie might be had of the declinations and places and consequently of the whole course and motion of the Sunne and that by comparing together so many observations the Sunnes Eccentricitie and Apogaeum might the more assuredly be known By knowledge whereof the way was laid open for the correcting and true making of the Tables of the Suns middle motions and Prosthaphaereses which were necessarie helps and means for calculating the Ephemerides of the Sun there set down without which the regiment or table of declination of the Sunne next following which I may commend as free from error observable at sea and seldome differing one minute from observation on land and for which principally all the former pains were undertaken could not so easily have been made Now if any shall think that most of this fourth part going before this regiment might have been omitted as being impertinent to the use of Mariners and exceeding their capacitie I answer that it was not my purpose neither could I in all places apply my self to the most part of sea-mens capacitie knowing many that would not be content with this regiment alone but that desired more to know the ground and root from whence this fruit grew whose desire I was also willing to satisfie as I could for the present having seldome had a more inconvenient season for such a purpose Then after some caution given concerning the use of this table of Declination and the Equation thereof in places farre differing in longitude from hence there followeth a Table of 32 principall fixed starres about the Aequinoctiall that have been most commonly known and observed by Seamen with their Declinations corrected and another Table of as many more of the notablest starrs about the North Pole is thereto annexed with their distances from the Pole corrected also and verified by diligent Observation on land To these is added a Table of the Suns Right Ascensions resolved into hours and minutes for every day of the year with the use thereof for finding at what houre any of those stars commeth to the Meridian at any time of the year that hereby the Mariner might find at all times when they come to the Meridian and so the easilier learn to know and observe them Hereunto I have newly adjoyned the description and use of an Instrument which way not unfitly be called a Sea-quadrant whereby is shewed how the height of the Sun at sea may by two observers be much more exctly observed then by any other means before published and how the height of the Pole may readily be found at any time of the night by observation of the Pole-star and Guard without making any abatement or allowance as the manner hath been in regard of the point of the compasse whereupon the Guard is situate But now for further satisfaction in every one of these particulars I refer the friendly Reader to the Treatise it self here following which Simon Stevins inconsiderate desire of finding fault with my Tables of Rumbs hath caused me to conclude with an Answer to him plainly shewing himself and not me to be in the same fault that he would find with me To this Treatise for the benefit of the younger and unskilfuller sort of Seamen it was thought not unmeet to adjoyn the short Treatise following containing the sum of the whole Art of Navigation first set forth in Spanish by Roderigo Samorano and since translated into English by a friend of mine for the benefit of our Nation which Treatise I would wish all them that are but New beginners in that Art first to peruse and understand well before they come to the reading of the former which for the reading thereof with the greater profit requireth such a one as is alreadie reasonably well acquainted with the rules and principles of that Art which I have not hitherto known to be more briefly and plainly nor yet more fully set down and published in any other book then they are in that little Treatise This notwithstanding I must admonish the Reader that in stead of the Sea-Chart therein described according to the common error with equal degrees of Latitude he follow that manner of making the same which I have in the former Treatise set down Chap. 3 4 5 and 6. And that in stead of the rules and allowances for finding the Latitude by the height of the Pole-star which are many waies and much
only 12 seconds hereof that is the Part Proportional answerable to the excesse of 9. sec. above 4 sec. Where Maginus after the Prutenick account maketh it to be in 0 degr 25 min. of Aries that is 33 minutes wanting of the truth found by Observation The like difference I have often found by many and diligent Observations especially for the space of the four years before mentioned the whole Catalogue of which Observations I thought good for thy further satisfaction herein to set down in a Table after I have first shewed with what Instrument and after what manner I Observed the same that if any error herein hath been committed it may the more easily appeare and be amended CHAP. XIX The description and use of a great Quadrant for Observation of the Sun on Land THe Instrument therefore wherewith I took those Observations was a Quadrant of more then six foot and a quarter semidiameter for the room wherein I was to use it could not well admit a greater quantity which by reason of his largeness was so exactly made and divided that both minutes and half minutes might therein be easily discerned The Limb and sides of the Quadrant were about two inches and a quarter in thickness the breadth of the Limb about four inches the breadth of the Sides about two inches and an half In the midst of the ends of one side of this Quadrant were two round holes made in either end one whereby the Quadrant was hanged like a gate on his hinges upon two round pins fitted to those holes and fixed in the ends of a copple of sockets put close upon a strong square post Perpendicularly erected and the upper end thereof fastned to the side of a principal rafter in an upper chamber where a window according to the Reclination of the Roof of the house was made between it and the next rafter in such sort that carrying your eye along by the circumference of the Quadrant you might by the Center thereof placed at the window see any part of the Heavens neer the Meridian from the Zenith to the Horizon The nether end of this post resting on the floor was put into the midst of a socket nailed to the floor which was so wide that on every side the post wedges might be put in to coyn it at pleasure this way or that way till the side of the Quadrant were found to stand exactly Perpendicular by the hanging of the plum-line all alongst most precisely upon a line Parallel to the Zenith line of the Quadrant To the Center of the Quadrant was fastned a strong Ruler of one inch in thickness two inches in breadth and almost six foot and an half in length carrying two Sights upon it viz. at either end one of equal breadth and length the end of the middle line of each Sight falling Perpendicularly upon the middle or fiducial line and plain Superficies of the Ruler Through the upper Sight placed at the Center was made a square hole as great as it could well be Through the midst of this Sight and hole was put a straight wyre erected Perpendicularly from the Fiducial line and plain of the Ruler and so much of it made flat and thin as was between the top and base of that square hole This wyer served for Observing the Stars the flat side whereof was to be turned towards the eye in Observing of great Stars and the narrow side or edge of it was turned to the eye-ward when smal Stars were to be Observed Through the midst of the nether Sight from the top of it to the Base thereof was made a narrow slit Perpendicularly erected likewise from the Fiducial line and plain of the Ruler and Quadrant When I Observed the Stars I looked through this slit Elevating and Depressing the Ruler till the wyer being first fitted to bigness of the Star did even cover the Star from my sight in such sort that I might see both edges of the Star alike on either side above and beneath the wyre The square hole in the Sight had a cover fitted to it like the cover of a box wherewith it was wholly covered when the Sun was to be Observed The nether end of the Ruler carrying the Sights was to be fastned with a screw-pin at any part of the Circumference of the Quadrant as need required With this Quadrant alwaies rectified by the Plumb line in time of Observation as before is shewed the height of the Sun was most easily and exactly Observed by turning the Quadrant this way or that away and Elevating or depressing the Ruler carrying the Sights till the top and sides of the shadow of the Upper Sight placed at the center fell upon the nether Sight placed at the center fell upon the nether Sight placed at the Circumference equidistantly from the top and sides thereof For then the upper edge of the Ruler sheweth precisely the height of the Sun desired in degrees and minutes upon the limb of the Quadrant saving that one whole degree was alwaies to be added thereto because the breadth of that part of the Ruler that lay upon the Limb of the Quadrant was made to be just equal to two degrees that is on either side one degree from the fiducial line Now for finding out the Meridian Altitudes of the Sun and Stars I first found the Meridian line thus with the quadrant rectified and used as before is shewed I Observed the height of the Sun in the forenoon and so warily letting the Quadrant stand immoveable and laying the side of a straight Ruler that was about seven foot in length close along to the perpendicular side of the Quadrant close by the end of that side of the Ruler touching the floor of the chamber I made a prick upon the floor Also laying the side of the Ruler to the perpendicular side and limb of the Quadrant I made in like manner another prick so far as conveniently I could from the former upon the floor close by the corner of that side of the Ruler By these two pricks I drew a right line which represented the intersection of the Suns Azimuth or of the continued plain of the Quadrant and of the plain of the floor in the time of Observation Likewise in the afternoon the Ruler of the Quadrant carrying the Sights being fixed in the same place where it was in time of Observation in the forenoon I Observed diligently till the Sun came to the same height that he had when I Observed in the forenoon which I did by following the motion of the Suns shadow with the Quadrant till the edges of the top and sides of the shadow of the upper Sight fell upon the nether Sight equidistantly from the top and Sides thereof Then carefully letting the quadrant stand immovable and drawing the line of intersection of the floor and Suns Azimuth in time of the afternoon Observation in like manner as I did in the forenoon setting one foot of the Compasses in the
Equinoctial And these Circles may be infinite between the Equinoctial and the North and South Poles and in the Sea-chart some of them are represented by the lines which are drawn from East to West And two of these Circles are the two Tropicks of Cancer and Capricorn which are the bounds of the Suns greatest Declinations Likewise all those Circles which the Sun and the stars in Heaven do by the motion of the first or highest moveable heaven describe from East to West are parallels and serve in the Sphere to shew the Latitude And when a ship saileth in the same height of the pole then she saileth in a parallel and runneth alwayes East or West Which manner of sailing we use at all such times when we find our ship in the height of that land to which we are going CHAP. XIX Of the Degrees EVery one of these Circles is divided into 360 equal parts which they call degrees and every degree is divided into other 60 equal parts which are called minutes which degrees and minutes are the common measure that we use in Navigation when we make any account in the Heavens either in taking the the height of the Sun and stars above the Horizon or in measuring the distance from our Zenith to the Equinoctial These degrees are marked in a line drawn from North to South in the most vacant part of the Sea-Chart This line in general Sea-Charts is divided into 90 equal parts which are counted beginning at the Equinoctial line from one to 90 both Northwards and Southwards And in those Charts which are not general this line hath such divisions as it is capable of according to the largenesse of the Chart beginning to make account from the Equinoctial CHAP. XX. What is meant by Longitude and Latitude THe Longitude of any place is a part of the Equinoctial or of some other parallel contained between two Meridians whereof one passeth by the Canary Islands and the other by the place given but if neither of the said Meridians passe by the foresaid Islands it is called respective Longitude And this respective Longitude is called in the Art of Navigation the distance or length of the right line which is determined or bounded by two other right lines running North and South of which two the one passeth by the Port or Haven from whence we set sail and the other by the place where our ship is And so shall the distance of the right line be the part of any right line whatsoever running East and West comprehended between the two foresaid right lines extended North and South The Latitude of a place is a part of any Meridian whatsoever contained between two parallels whereof one is the Equinoctial and the other the parallel of the place given This Latitude the Mariners do call the Distance from the Line understanding by the Line the most principal of all others which are drawn in the Chart that is the Equinoctial Line They use also to call it the heighth which is as much to say as the heighth of the Pole above the Horizon And so the Distance from the Equinoctial shall be a part of any North and South Line contained between the Equinoctial and any line running from East to West which passeth in the graduation of the Chart by the same degree of Latitude in which we find our selves to be 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 TO know the Latitude or distance from the Equinoctial line there are required five things whereof any one being wanting we cannot possibly finde out how far we are distant from the said Line And these are the Astrolabe or Quadrant the height of the Sun the Shadows the Declination the Regiment or Rules of the Sun The Astrolabe is to be made after this manner In the midst of a round plate or table of mettal or wood being smooth and plain every where and about a finger thick you shall take the center A wherein having placed one foot of your compasses you shall with the other draw as great a circle as conveniently you can in the said Table And within this Circle must be drawn two other Circles the one distant from the other about the breadth of a grain of wheat and the third must be distant from the second twice so much as the second is from the first And your Ruler being laid just to the center A you shall draw the line BAC which divideth every one of the three circles into two equal parts And putting one point of your compasses standing open according to the length of the line BC upon the point C where the greatest Circle is divided by the line BC with the other point you shall draw above the point D a part of a Circle and another under E. And then putting one foot of the compasses thus opened upon the point B you shall draw other two parts of a Circle which will crosse the first in F and G. And your Ruler being laid to F and G you shall draw the line DE which must passe by the center A. Then let the Quadrant DB be divided into 3 equal parts and every one of those into three other parts and each of those nine into two and every one of those 18 into 5 and so the said Quadrant shall be divided into 90 equal parts or degrees Unto which degrees shall be placed the numbers belonging to them from 5 to 5 between the second and the third circle beginning from B and ending with 90 at the point D. Then let there be made at the point D a little hole upon the line DE through which may be put a little ring or some strong riband or string and you shall make a knot thereon whereby your finger may take hold and the Astrolabe hanging by that hole you shall put through a slender threed with a plummet of lead which may hang quite under the Astrolabe which threed if while the Astrolabe hangeth immoveable it fall just upon the line DE then is the Astrolabe well rectified If not you must continue cutting off some thing and lightning that side towards which the thred doth fall until it hang even with the foresaid line Then must you draw upon a Ruler of the same matter being about a finger and an half broad the right line HI along through the very midst of the breadth thereof which Ruler shall be made after the same fashion that here is set down cutting away from one half of the length half of the breadth alwayes saving whole the line HI And so likewise shall you cut off along the half of the length on the contrary part half of the breadth so that the line HI may remain whole on that side also And neer to the ends of the said Ruler you shall set two little square Vanes of the breadth
that the rose or fly may play more nimbly upon the pin This pin must be made of lattin with a very sharp point and is to be fastned upright in a round box of wood which must be of the fashion of a great cup-dish containing the rose within it being covered above with a clear round glasse and the joynts thereof must be stopped with wax to the end that no wind may enter into the rose to disturb it There must be great care had that this rose with the wires placed upon the pin may go nimbly and may not swerve more to the one side then to the other but may stand even and level And when it inclineth towards either part you must put on the contrary part a little wax or a thin plate of lead fastened under the pastboard which covereth the wires This box wherein the rose plaieth up and down hangeth within two hoops of lattin which are two round circles inclosed one within another and distant asunder by the space of half a fingers breadth with two nails of lattin which are diametrally opposite And the box being fitly placed within these hoops you must make in the outward hoop two holes which must be distant from the foresaid two nails a quarter of a Circle both wayes And by these two holes must the outward hoop or circle be fastened within a square box or a round so as although that uttermost box be tossed up and down every way with the motion of the ship yet alwayes the superficies and glasse of the inner box may lie level with the Horizon And this being done with care the instrument which they call the Sea-Compasse is fully finished The manner of using the same is when being placed with the box in the midst of the poop of the ship where the bittacle standeth in a right line which passeth from the bolt-sprit by the midst of the main mast to the poop it serveth continually to govern the ship by moving of the Rudder till the winde or the line of your Compass towards which we desire to shape our course stand directly towards the prow or bolt-sprit of the ship They use also for the night to mark a point within the inner part of the inner box which in respect of the capitel of the Compasse may stand directly towards the prow of the ship And alwayes in guiding the ship you must take heed that the said point be continually joyned with the winde of the rose towards which you intend your course CHAP. XVIII How the Variation of the Compasse may be found THe Mariners use to examine whether their Compass North-easteth or South-westeth watching for that purpose when the former guard beareth with the North star North-east and South-west taking a little of the point of North and South And placing their Compasse in an open place where the North star may be seen if the flowerdeluis of the Rose looketh directly towards the star their Compasse varieth nothing at all but if the star be to the North-east so much as it varieth from the point of the flowerdeluis so much the Compass North-westeth and if it varieth to the North-west of the Compass how much the star swerveth from the point of the flowerdeluis so much the Compasse North-easteth And in regard of this variation of the Compasse there must alwayes allowance be made in the course which is holden This manner of finding out the variation I do account to be somewhat subject unto errour but at land there is another more certain way by the Meridian line which is to be taken in manner following The finding of the Meridian-line In a superficies which is plain and level every where and in a place where the Sun shineth at his rising and setting you must draw certain circles upon one center and having pitched a stile upright in the same center the head whereof must be approved with a pair of compasses to be equally distant from all parts of one of those circles observe you in the morning two or three hours before noon when the point of the shadow of the stile toucheth the circumference of any of those circles and having made a mark in the touches take diligent heed in the afternoon also when the same point of the shadow turneth about to touch in the same circle and making another mark in that second touch divide in the midst that part of the circle which is between those two marks Then laying your Ruler upon the point of the division and upon the center of those circles draw a line which shall be your Meridian and the true North and South Rumb upon which setting your compasse and laying your Ruler over the glasse that it may passe along over the Meridian and over the center or capitel of the rose or flie eithe said Ruler lieth over the North and South of the Compasse and then is the Compasse without variation or the Ruler declineth toward the North-east or South-west and how much it declineth that way so much the Compasse North-westeth or else it declineth towards the North-west and then it North-easteth so much as the Ruler declineth that way But to know the variation of the Compasse both at land and sea we will deliver another far more easie and certain way when we come to intreat of the universal Dial. CHAP. XIX Of the Sea-chart THe Sea-chart is nothing else but a lively picture of the earth and water And it containeth five notable things which do concern as well the true making of the Chart as also the inabling of the Mariner to know the way which he maketh the place where he is and the end of his journey The first is the laying out of the Coasts of the Land which that it may be truly done it is meet that every thing be set down in the Chart in the same course distance and heighth that shall be found in Navigation The second is that it containeth not onely the coast of the firm land but also all other particularities which do occur in sailing as namely Islands Iselets Banks or Bars Shoalds Rocks and Flats The third is the lines which signifie the 32 winds by the help whereof we may see whether the parts of the land be well laid out and in their true courses one from another And of these winds the black are the eight principal which are called whole winds The green be half winds or half parted winds and the red be the quarters of the winds You may know in your Chart whether these winds be well drawn if you trie with your compasses that all points of them be equally distant one from another and that all winds representing the same Rumb be parallels As namely that one Northeast and Southwest Rumb be parallel to another Northeast and Southwest Rumb The fourth is the graduation in all parts whereof it is meet that the degrees be equal one to another and that the parts of the land do directly lie East
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
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