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
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
Aequinoctial then the secans of that Parallels latitude hath to the whole sine But in this table it was thought sufficient to use such exactness as that thereby in drawing the lineaments of the nautical planisphaere sensible error might be avoided He that listeth to be more precise may make the like table to decades or tennes of seconds out of Ioachimus Rhaeticus his Canon magnus triangulorum Notwithstanding the Geometrician that desireth exact truth cannot be so satisfied neither for whose sake and further satisfaction I thought good to adjoyn also this Geometrical conceit of dividing a Meridian of the nautical planisphaere Let the Aequinoctial and a Meridian be drawn upon a Globe Let the Meridian divided into degrees minutes seconds c. roul upon a streight line beginning at the Aequinoctial the Globe swelling in the mean time in such sort that the Semidiameter thereof may be alwaies equal to the secans of the angle or arch conteined between the Aequinoctial and Semediameter insisting at right angles upon the foresaid streight line The degrees minutes seconds c. of the Meridian noted in the streight line as they come to touch the same are the divisions of the Meridian in the nautical planisphaere And this conceit of dividing the Meridian of the nautical planisphaere may satisfie the curious exactness of the Geometritian but for mechanical use the table before mentioned which here now followeth may suffice This Table serving principally for the true dividing of the Meridians of the Sea Chart in such sort that in any part thereof a minute of the Meridian shall have the same proportion to a minute of the Parallel thereto adjoyning that it hath in the Globe may not unfitly be called A Table of Latitudes For as in Geographie the latitude of a place is nothing else but the shortest distance thereof from the Aequinoctial line measured upon the convexitie of the earth or sea in degrees and minutes and therefore Tables containing such distances are ordinarily called Tables of Latitudes So this Table shewing the distance of every minute of a Meridian in the Sea Chart from the Aequinoctial line thereof towards the North or South in such equal parts whereof one minute of the Aequinoctial is supposed to contain 10,000 may with like reason by a certain analogie and resemblance it holdeth with the foresaid tables be very well called A Table of Latitudes of every minute of a Meridian of the Sea Chart in such parts whereof each minute of the Aequinoctial containeth 10,000 This Table is divided into three columnes whereof the first containeth in the head thereof the degrees and in the rest of that columne minutes of a Meridian of the nautical planisphaer beginning at the Aequinoctial line In the second columne are placed equal parts of the same Meridian beginning likewise to be numbred from the Aequinoctial of which parts each minute of the Aequinoctial is supposed to contain 10,000 and sheweth how many of these parts each minute of latitude in the Sea Chart must be distant from the Aequinoctial The third columne sheweth the differences of the numbers set down in the second columne The use hereof followeth after this Table A Table of Latitudes c. Min. 0 Degr.  1 Degr.  2 Degr.  3 Degr.  Equal parts of a Merid. Difference of equ par Equal parts of a Merid. Difference of equ par Equal parts of a Merid. Difference of equ par Equal parts of a Merid. Difference of equ par 0 00.000 10.000 600.012 10.001 1.200.196 10.006 1.800.749 10.013 1 10.000 10.000 610.013 10.001 1.210.202 10.006 1.810.762 10.014 2 20 000 10.000 620.014 10.001 1.220.208 10.006 1.820.776 10.014 3 30.000 10.000 630.015 10.001 1.230.214 10.006 1.830.790 10.014 4 40.000 10.000 640 016 10.001 1.240.220 10.006 1.840.804 10.014 5 50.000 10.000 650.017 10.001 1.250.226 10.006 1.850.818 10.014 6 60 000 10.000 660.018 10.001 1.260.232 10.006 1.860.832 10.014 7 70 000 10.000 670.019 10.001 1.270.238 10.006 1.870.846 10.014 8 80.000 10.000 680.020 10.002 1.280.244 10.007 1.888.860 10.015 9 90.000 10.000 690.022 10.002 1.290.251 10.007 1.890.875 10.015 10 100 000 10.000 700.024 10.002 1.300.258 10.007 1.900.890 10.015 11 110 000 10.000 710.026 10.002 1.130.265 10.007 1.910.905 10.015 12 120.000 10.000 720.028 10.002 1.320.272 10.007 1.920.920 10.015 13 130.000 10.000 730.030 10.002 1.330.279 10.007 1.931.935 10.015 14 140·000 10.000 740.032 10.002 1.340.286 10.007 1.940.950 10.016 15 150.000 10.000 750.034 10.002 1.350.293 10.007 1.950.966 10.016 16 160.000 10.000 760.036 10.002 1.360.300 10.007 1.960.982 10.016 17 170.000 10.000 770.038 10.002 1.370.307 10.008 1.970.998 10.016 18 180.000 10.000 780.040 10.002 1.380.315 10.008 1.981.014 10.016 19 190.000 10.000 790.042 10.002 1.390.323 10.008 1.991.030 10.016 20 200.000 10.000 800.044 10.002 1.400.331 10.008 2.001.046 10.017 21 210.000 10.000 810.046 10.002 1.410.339 10.008 2.011.063 10.017 22 220.000 10.000 820.048 10.002 1.420.347 10.008 2.021.080 10.017 23 230.000 10.000 830.050 10.002 1.430.355 10.008 2.031.097 10.017 24 240.000 10.000 840·052 10.003 1.440.363 10.008 2.041.114 10.017 25 250.000 10.000 850.055 10.003 1.450.371 10.009 2.051.131 10.017 26 260.000 10.000 860.058 10.003 1.460.380 10.009 2·061 148 10.018 27 270.000 10.000 870.061 10.003 1.470.389 10.009 2·071 166 10.018 28 280.000 10.000 880.064 10.003 1.480.398 10.009 2·081 184 10.018 29 290.000 10.000 8â—0 067 10 00â— 1.490.407 10.009 2·091 201 10.018 30 300.000 10.000 900.070 10.003 1.500.416 10.009 2.101.220 10.018 31 310.000 10.000 910.073 10.003 1.510.425 10.009 2.111.238 10.019 32 320.000 10.000 920.076 10.003 1.520.434 10.009 2.121.257 10.019 33 330.000 10.000 930.079 10.003 1.530.443 10.010 2.131.276 10.019 34 340.000 10.000 940.082 10.003 1.540.453 10.010 2.141.295 10 019 35 350.000 10.000 950.085 10.003 1.550.463 10.010 2.151.314 10.019 36 360 00â— 10 000 960.088 10.003 1.560.473 10.010 2.161.333 10.019 37 370 00â— 10.000 970.091 10.004 1.570.483 10.010 2.171.352 10.020 38 380.000 10.000 980.095 10 0â—4 1.580.493 10.010 2.181.372 10.020 39 390.000 10.000 990·099 10.004 1.590.503 10.010 2 191 392 10.020 40 400.000 10 0â—0 1.000.103 10.004 1.600.513 10.010 2.201.412 10.020 41 410.000 10.000 1.010.107 10.004 1.610.523 10.011 2.211.432 10.021 42 420.000 10.000 1.020.111 10.004 1.620.534 10.011 2 221.4â—2 10.021 43 430.000 10.000 1.030.115 10.004 1.630.545 10.011 2.231.473 10.021 44 440.000 10 000 1.040.119 10.004 1.640.556 10.011 2.241.494 10.001 45 450.000 10.000 1.050.123 10.004 1.650.567 10.011 2.251.515 12.021 46 460.000 10.000 1.060.127 10.004 1.660.578 10.011 2.261 536 12.021 47 470.000 10.000 1.070.131 10.004 1.670.589 10.011 2.271.557 11.002 48 480.000 10.001 1.080.135 10.005 1.680.600 10.012 2.281.570 10.022 49 490.000 10.001 1.090.140 10.005 1.690.612 10.012 2.291.601 10.022 50 500 00â— 10.001 1.100.145 10.005 1.709.624 10.012 2 301.62â— 10.022 51 510.000 10.001 1.110.150 10.005 1.710.636 10.012 2.311.645 10.022 52 520.000 10.001 1.120.155 10.005 1.720.648 10.012 2.321.667 10.023 53 530.000 10 001 1.130.160 10.005 1.730.660 10.012 2.331.690 10.023 54 540.000 10.001 1·140 165 10.005 1.740.672 10.012 2.341.713 10.023 55 550.000 10.001 1.150.170 10.005 1.750.684 10.013 2.351.736 10.023 56 560.000 10.001 1.160.175 10.005 1.760.697 10.013 2.361.759 10.023
with the Regiment of the Sun and of the star the rules of the Moon and of the Tides the declaration of the Sea-chart and other things appertaining hereunto CHAP. I. The Definition of the Sphere A Sphere is a solid or massie body without hollownesse and perfectly round in the midst whereof there is a prick called the center by which there passeth a right line named the Axtree and the points where this line endeth upon the superficies of the whole body are called Poles because upon them the Sphere is moved CHAP. II. That the whole World is a Sphere AND so it is evident that the whole frame of the World wherein we live is a Sphere being as it is solid so that in the whole World there is no empty place also it is perfectly round upon the upper Superficies of the highest heaven and it hath in the very midst a certain point to wit the center of the earth by which we do imagine a right line or Axtree to passe from one pole to another upon which the World is moved about from East to West CHAP. III. Of the division of the Sphere THE whole Sphere of the World is divided into two parts or Regions the Elementary and Celestial The Elementary part or Region hath four parts the first whereof is the earth which together with the element of water which is the second maketh one perfect Globe and round about both these are two other elements namely the Air and above that the fire which filleth the space between the Air and the Sphere of the Moon of which Elements by vertue of the heat of the Heavens are made and compounded all corruptible things in the world The celestial Region consisteth of other ten parts the first whereof is the Sphere of the Moon the second the Sphere of Mercury the third of Venus the fourth is the Sphere of the Sun the fifth of Mars the sixth of Jupiter the seventh of Saturn the eighth is the Sphere of the fixed stars which is called the Firmament the ninth is the Crystalline heaven and lastly the tenth and highest is the Sphere called the Primum mobile that is the first or highest moveable heaven That which remaineth called the Empyreal heaven because it hath no motion cometh not to be considered on in the Art of Navigation A Figure wherein may be seen the Composition of the whole Sphere of the World CHAP. IV. Of the motion of the Heavens THe number of the Heavens is known by the motions observed in them which are ten distinct one from another For the Moon moveth her proper and peculiar motion in 27 dayes and 8 hours which is one Revolution Mercury Venus and the Sun finish their motion in one year which conteineth 365 dayes and almost a quarter of a day Mars runneth his course in two years Jupiter in twelve years Saturn in thirty years the eight Sphere according to the opinion of some in seven thousand years the ninth in five and twenty thousand and eight hundred years and the tenth in four and twenty hours almost Which ten motions are reduced unto three principal the first is that of the first moveable upon the two ends of the Axletree which are called the Poles of the World from East to West turning about again unto the East in 24 hours and this Sphere by the force of his motion carrieth about with it all the other lower Spheres in the space of 24 hours Howbeit they move also the contrary way with a second motion which is from West to East upon two other poles distant from the first about three and twenty and an half such parts whereof the whole compasse of heaven conteineth three hundred and sixty And this second motion is accomplished in each of the lower Heavens in divers spaces of time as is before said The third motion is proper to the eighth Heaven wherein the fixed stars are placed which motion is the cause that the distance of the poles of the first motion from them of the second motion doth vary being sometimes greater and sometimes lesse CHAP. V. Of the Figure of the Heavens THat the Heavens are round it is proved because roundnesse is the most perfect Figure of all others being whole and intire having no need of any joynts being also of the greatest capacity of all figures that have the same compasse and in that respect most fit to contain all other things Also the principal bodies of the World as the Sun the Moon and the stars are of this Figure and we see the same likewise in those things which are bounded by themselves as it is manifest in drops of water and all other liquid things CHAP. VI. That the Earth and Water make one perfect Globe THere is nothing that sheweth more cleerly that the earth and water make one round Globe then the shadow which they make in the Eclipses of the Moon which shadow we alwayes see to be a part of a circle For if the body which is the cause of the same shadow were three-square or four-square the shadow it self also would appear in the same fashion Wherefore the shadow of these two bodies together being round it is manifest that they are round also CHAP. VII That the Earth is in the center of the World ONe sign we have to be assured that the Earth is in the midst and center of the World namely that wheresoever we are upon the face of the earth we alwayes see one half of the Heavens the other half being hidden out of our sight Moreover the stars in what part of the Heavens soever they be either in the East West or South we see that they are alwayes of the very same bignesse Whereby we may easily perceive that they are alwayes equally distant from our sight and whereas they move round about it it followeth that we are upon the center of that body on whose superficies the said stars describe their circles CHAP. VIII The whole quantity of the Earth ANd albeit the Globe of the Earth and Water compared with the Spheres of the Stars is as it were a center or prick yet being considered by it self it conteineth in the greatest circle thereof 6300 common Spanish leagues Which a man may easily perceive by taking two such points or head-lands of the earth as are under the same Meridian and which differ in distance one from another so much as one of those parts is whereof the compasse of the whole world conteineth 360 and it is found both by Navigation at Sea and also by travel on land that the two foresaid points are distant each from other 17 leagues and an half of which leagues each one conteineth 4000 paces every pace 5 foot every foot 16 fingers and every finger 4 grains of barley CHAP. IX Of the Equinoctial Circle BEing to treat of the Circles of the Sphere of the World the first which offereth it self to be spoken of is the Equinoctial Circle by means whereof we do know in