05 31 19 73 10 31 11 73 15 31 03 73 20 30 55 73 25 30 47 73 30 30 39 73 35 30 31 73 40 30 22 73 45 30 14 73 50 30 06 73 55 29 58 74 00 29 50 74 05 29 42 74 10 29 34 74 15 29 26 74 20 29 18 74 25 29 10 74 30 29 01 74 35 28 53 74 40 28 44 74 45 28 36 74 50 28 28 74 55 28 20 75 00 28 11 75 05 28 03 75 10 27 55 75 15 27 46 75 20 27 38 75 25 27 29 75 30 27 21 75 35 27 12 75 40 27 04 75 45 26 56 75 50 26 47 75 55 26 39 76 00 26 30 76 05 26 22 76 10 26 13 76 15 26 05 76 20 25 26 76 25 25 47 76 30 25 39 76 35 25 30 76 40 25 22 76 45 25 13 76 50 25 04 76 55 24 56 77 00 24 46 77 05 24 38 77 10 24 30 77 15 24 21 77 20 24 12 77 25 24 03 77 30 23 55 77 35 23 46 77 40 23 37 77 45 23 28 77 50 23 20 77 55 23 11 78 00 23 02 78 05 22 53 78 10 22 44 78 15 22 35 78 20 22 26 78 25 22 17 78 30 22 08 78 35 21 59 78 40 21 51 78 45 21 41 78 50 21 33 78 55 21 24 79 00 21 15 79 05 21 06 79 10 20 57 79 15 20 47 79 20 20 28 79 25 20 29 79 30 20 20 79 35 20 11 79 40 20 02 79 45 19 53 79 50 19 44 79 55 19 35 80 00 19 26 80 05 19 16 80 10 19 07 80 15 18 58 80 20 18 49 80 25 18 40 80 30 18 30 80 35 18 21 80 40 18 12 80 45 18 02 80 50 17 53 80 55 17 44 81 00 17 35 81 05 17 25 81 10 17 16 81 15 17 07 81 20 16 57 81 25 16 48 81 30 16 38 81 35 16 29 81 40 16 20 81 45 16 10 81 50 16 01 81 55 15 52 82 00 15 42 82 05 15 33 82 10 15 23 82 15 15 14 82 20 15 04 82 25 14 55 82 30 14 45 82 35 14 36 82 40 14 26 82 45 14 17 82 50 14 07 82 55 13 58 83 00 13 48 83 05 13 39 83 10 13 29 83 15 13 19 83 20 13 10 83 25 13 00 83 30 12 50 83 35 12 40 83 40 12 31 83 45 12 21 83 50 12 12 83 55 12 02 84 00 11 52 84 05 11 43 84 10 11 33 84 15 11 23 84 20 11 13 84 25 11 04 84 30 10 55 84 35 10 44 84 40 10 34 84 45 10 24 84 50 10 14 84 55 10 05 85 00 09 55 85 05 09 46 85 10 09 36 85 15 09 26 85 20 09 16 85 25 09 06 85 30 08 57 85 35 08 47 85 40 08 37 85 45 08 27 85 50 08 17 85 55 08 07 86 00 07 58 86 05 07 48 86 10 07 38 86 15 07 28 86 20 07 18 86 25 07 08 86 30 06 59 86 35 06 49 86 40 06 39 86 45 06 29 86 50 06 19 86 55 06 09 87 00 05 59 These TABLES of Latitude Longitude and Inclination may make Tryal whether the Places in them be truly Scituated in the Mapps or not for if the Inclination be not the same that it is in this TABLE they are not and then by the Inclination that they observe and the help of the CAROLINE TABLES for Longitude they may be Corrected as it is plain ly the Examples in the Treatise before The Longitudes East and West in the Tables are to he accounted from LONDON A TABLE of the Latitude Longitude and the Inclination of the Inclinatorie Magnetical Needle in some of the most eminent Places of the World in 1676. Â Â d. m. Â Japan Latitude 038 00 North. Longitude 143 20 East Inclination 063 53 North. Bantam Latitude 006 15 South Longitude 120 50 East Inclination 022 53 South Malacca Latitude 001 41 North. Longitude 110 50 East Inclination 005 42 South The North end of Sumatra Latitude 005 28 North. Longitude 111 15 East Inclination 001 44 North. The River of Bengale Latitude 022 09 North. Longitude 116 09 East Inclination 031 09 North. Cape Canoun Latitude 07 50 North. Longitude 92 15 East Inclination 11 23 North. Suratt Latitude 21 00 North. Longitude 94 12 East Inclination 33 43 North. The South end of St. Lawrence Latitude 25 37 South Longitude 55 30 East Inclination 39 01 South The Cape of Good Hope Latitude 35 30 South Longitude 27 30 East Inclination 47 38 South St. Elena Latitude 16 03 South Longitude 04 44 East Inclination 15 29 South St. Elena Nov. Latitude 16 03 South Longitude 14 24 East Inclination 16 23 South Sampson 's River Latitude 04 22 North. Longitude 30 28 East Inclination 22 09 North. Old Calibar Latitude 04 50 North. Longitude 19 51 East Inclination 23 09 North. New Calibar Latitude 04 40 North. Longitude 18 12 East Inclination 23 06 North. River of Gambo Latitude 12 47 North. Longitude 07 41 West Inclination 37 54 North. Cape de Verd Latitude 14 25 North. Longitude 12 21 West Inclination 58 28 North. Tangier Latitude 35 36 North. Longitude 03 35 West Inclination 62 39 North. Gibralter Latitude 36 40 North. Longitude 03 18 West Inclination 63 29 North. Malago Latitude 36 45 North. Longitude 02 17 West Inclination 63 33 North. Alegant Latitude 38 20 North. Longitude 01 50 East Inclination 65 10 North. Leagorn Latitude 43 28 North. Longitude 12 39 East Inclination 68 01 North. Galipolie Latitude 40 08 North. Longitude 21 40 East Inclination 65 03 North. Rome Latitude 41 50 North. Longitude 15 45 East Inclination 66 43 North. Naples Latitude 41 08 North. Longitude 17 27 East Inclination 66 05 North. Venice Latitude 45 37 North. Longitude 17 21 East Inclination 69 17 North. Constantinople Latitude 40 56 North. Longitude 35 09 East Inclination 64 35 North. Alexandria Latitude 30 40 North. Longitude 36 04 East Inclination 55 39 North. Tunis Latitude 36 30 North. Longitude 03 54 East Inclination 63 05 North. Argier Latitude 36 40 North. Longitude 05 30 Â Inclination 63 14 North. Middle of Cyprus Latitude 34 18 North. Longitude 37 45 Inclination 58 54 North. Middle of Candia Latitude 35 08 North. Longitude 28 32 East Inclination 60 29 North. Middle of Corsica Latitude 42 05 North. Longitude 28 32 East Inclination 67 08 North. Middle of Scisilia Latitude 37 42 North. Longitude 16 45 East Inclination 63 26 North. Maiyork Latitude 39 38 North. Longitude 05 48 East Inclination 65 32 North. Cales Latitude 36 22 North. Longitude 04 00 West Inclination 63 16 North. Lisbon Latitude 39 08 North. Longitude 06 30 West Inclination 65 28 North. Cape Finister Latitude 43 10 North. Longitude 08 19 West Inclination 69 07 North. Burdeaux Latitude 45 10 North. Longitude 00 20 East Inclination 69 26 North.
any other place within Our Dominions and all other Our Officers and Ministers whom it may concern are to take particular notice That due obedience be given to this Our Royal Command Given under Our Signet and Sign Manual at Our Court at White-hall the Twenty Eighth day of June in the Eight and Twentieth year of Our Reign 1676. By His MAJESTIES Command Vera Copia Joseph Williamson The LONGITVDE Found WHereas of late dayes there hath been pretending for Longitude I shall not trouble my self with contradicting any of their wayes but shew a way which Almighty God hath made known to me and hath been proved by Observation in remote parts of the World There hath been some in former dayes that have thought they could find the Latitude of any place by the Inclination of the Inclinatory Magnetical Needle under the Horizon wherein they were much deceived because the Magnetical Needle respects its own Poles I mean the Inclinatory Needle and not the Poles of the World except it be in one Meridian in two opposite points Yet I honour their Names and Memories viz. Dr. Gilbert Physician in ordinary to Queen Elizabeth and Mr. Barlow of Winchester because they made known to the World their Opinions of that which they knew in their time And although the Inclinatory Needle cannot shew the Latitude because there is one and the same Inclination in a hundred several Latitudes yet it shews something else which is a means to find the Longitude which I shall shew and prove in my further Discourse In the mean time I am sorry that any one should be so impudent in our dayes to put it out in Print the Latitude may be found by the Inclination of the Inclinatory Needle and Mr. Edward Wright's Table of Inclinations in his Book of the Correction of Errors in Navigation if that had been for that use it had been made use of many years before he was born that hath put it out in Print Mr. Edward Wright in the latter end of his Book of the Correction of Errors in Navigation sets down several Reasons as he thought against Magnetical Poles but I shall make it manifest from Eighty five years Observations that there are two Magnetical Poles the one North and the other South I wrote in the Sea-mans Kalendar above Thirty years since that there were and that I knew their Latitude their Longitude and their Annual Motion which Motion of theirs is the cause of the Variating of the Variation of the Magnetical Needle or Compass and the cause of the Alteration of the Inclinatory Needle I did in that Kalendar foretel Twenty Years before it came to pass that in the Year 1657 there would be no variation at all at London which was found to be so and since it hath been Westerly and will be Three hundred Years after 1657. Mr. William Burrowes in his Tract of the Variation of the Compass had some thoughts of Magnetical Poles and hath some Calculations to find their Distance from the Poles of the World but his mind was that they were or rather the North Magnetick Pole was farther from the Zenith of London than the Pole of the World and makes the North Magnetick Pole to be 25 d. 44 m. from the Pole of the World Besides he had some thoughts of a Point respective in the Bowels of the Earth But when I had read him and considered of it I thought the Magnetick Pole might be nearer to the Zenith of London than the Pole of the World and that by the Latitudes of London and Vaygats and their Difference of Longitude 58 d. 00 m. and the Variation at London 11 d. 15 m. East and the Variation at Vaygats 7 d. 00 m. West I might find out the Magnetical Pole at M as in the following Scheme But here we must take notice that Mr. Burrowes Observations of the Variation at Vaygats was not the same year that he observed at Lymehouse in October 1580. but four years before as it plainly appears to me by the motion of the Magnetical Poles for he was one that Sailed much into those Northern Parts His Observation of the Variation at Vaygats was in the year 1576 and then the Variation at London was 11 d. 34 m. but in the year 1580 when it was 11 d. 15 m. at London it was 8 d. 38 m. at Vaygats as it appears in the following Scheme For finding the Latitude of the Poles we have in the Triangle L P V the co-latitude of London L P 38 d. 28 m. and P V the co-latitude of Vaygats 20 d. 00 m. and the Angle L P V ferè 58 d. 00 m. the Difference of Longitude between London and Vaygats To find the Side L V the Distance between London and Vaygats and the Angles P L V and P V L from P L V Substract 11 d. 15 m. and there remains the Angle V L M. And substract 8 d. 38 m. from P V L and there will remain the Angle L V M. Then in the Triangle L M V we have the Side L V and the Angles L M V and M V L to find the Sides L M and V M the Distances of the Magnetical Pole from the Zenith of London and the Zenith of Vaygats And lastly we have in two Triangles viz. PLM and P V M two Sides and one Angle included to find P M the Distance of the Magnetical Pole from the Pole of the Earth 8 d. 30 m. The finding of the motion of these Magnetical Poles was by the decreasing of the Variation Which was first found to decrease by Mr. John Mair Secondly By Mr. Edmund Gunter Professor of Astronomy at Gresham Colledge in London Thirdly By Mr. Henry Gellibrand the next Professor of Astronomy after Mr. Gunter Fourthly By my self in 1640. And lastly By Mr. Robert Hooke and others in 1665. The encrease of it Westerly as it shall hereafter be declared it cost me much time in Calculation before I could satisfie my self in it Before I come to declare the motion of these Magnetick Poles I shall make two Queries First Where these Poles are Secondly The Cause of their motion For Answer to the first Out of doubt they are in the Magnetick Sphere that environeth or compasseth the whole Earth Fig. I Although we have found out that which Mr. William Burrowes did not think of yet we must not forget him for that which he did because by his Observations we come to find out the places of the Magnetick Poles as it appears in the Scheme above Their Period or Revolution is Six Hundred years which is Two Hundred and Thirty years more than Henry Philips doth allow them in the Sea-mans Kalendar Their yearly motion is six Tenths of a Degree that is Thirty six Minutes which I thus prove Substract 1580 out of 1657 the remainer is 77 Years which multiply by six Tenths the Product will be 46 2 10 which was the Angle at the Pole of the World M P L in June 1580. From June
in Print that in 1666 he did Observe at the Hermitage in Wapping with a large Quadrant and found the Variation to be forty one minutes How large soever his Quadrant was his Understanding in this Business was very little and I fear something else less The Variation here at London in June 1666 was 1 d. 35 m. and 36 sec I know not what Title to give to that forty one Minutes Observer except it be Mr. Impudent Ignoramus Fig. II. As the Horizontal Needle hath a double motion about the Round Loadstone or Terrula so also the Inclinatory Needle hath a double motion about the Earth as it plainly appeareth in the Diagram following Wherein let A be the Center of the Earth and B C D the one half of the Magnetical Sphere B A D the Axis of it B the North Pole of it and D the South Pole A C the Equator of it or the Magnoctial or rather a Representation of the one half of it E F the Inclinatroy Needle in his Ring F the North End of it and E the South End The Needle on the Magnequator at C is parallel to the Magnetical Axis B A D but being moved forwards towards B unto G the North End F inclines downwards and so would the South End E if it were moved towards D. So there are two motions one of the Instrument and another of the Needle and so it will be at I and at K until you come to B the North Magnetical Pole FIG II. there will be continually one motion of the Instrument a Quadrant from C to B on the Center of the Earth and a motion of the Needle a Quadrant from V to F at the North Magnetical Pole of the Earth and then the South End of the Inclinatory Needle will be upwards to the Zenith and the South Point of the Horizontal Needle will be to the North Pole of the Earth One of late was questioning in what part or what Distance these Magnetical Poles were from the Earth I answer They are very near to the Body of the Earth because the nearer the Magnet the greater the strength Something is to be considered concerning those Variations of the Horizontal Needle that are not according to the situation of the place from the Magnetical Poles but are contrary as all the West-Indies according to the Poles they should be Easterly and they are Westerly which is by some accidental Cause in the Earth and their Motion as I have formerly said a forced Motion and not Natural These Variations must be alwayes the same except we will say one piece of the Earth moves from another which were very absurd If the Inclinatory Needle be fitted as it ought to be to turn Horizontally as the Horizontal Needle doth it will find an amplitude or an Azimuth as well as the Azimuth-Compass and hath been so used by Capt. John Wood now Captain of His Majesties good Ship Bone-Adventure If the Inclinatory Needle be not fitted to do the same that the Horizontal Needle doth it is not worth a straw to be made use of for the Inclination and therefore it is an Instrument of that curiosity in the making that it is not for such an one that will run headlong to make any thing although he neither understand nor know whether it be right or wrong nor cares not so he may get Money by it In the Year 1665. my Son Henry Bond sailed to the East-Indies in the good Ship the Greyhound of London I sent by him an Inclinatory Needle of five inches long in a Brass Ring fitted as it ought to be to observe with it on the Land and in the Year 1667 I wrote to him that the Inclination of the Needle at Ballasore the place where they were was 32 d. 10 m. and that the Variation was 7 d. 32 m. West When he came home he did acknowledge the Inclination was 32 d. 15 m. and the Variation 7 d. 30 m. by their Azimuth-Compass Now by this it is plainly evident that if by the Longitude of any place from the Magnestical Colure the Inclination may be found then the Longitude of any place from the Magnestical Colure may be found by the Inclination and by that the Difference of Longitude between any two places on the Earth I did write in the Sea-mans Kalendar above Thirty Years since that without doubt the Longitude would be found by the Observation of something below the Moon I have an Observation that was made by Mr. James Moorcock above Thirty Years since at Cape Charles on the Coast of Virginia which Observation of his doth very near agree to my Calculation now notwithstanding it be so long since and I have forgotten the Year when the Observation was made and therefore in finding of the Longitude I shall make use of my Inclination But to give the better satisfaction to the World I shall set down his Observation and my Calculation for this present time Mr. Moorcock's Observation of the Inclination somewhat above 60 d. 00 m. Bond 's 59 d. 50 m. Here we may take notice that although the Alteration of the Inclination be but slow when it hath been at the greatest or least at any place as here at London since it was at the greatest in 1657 it is altered not full six Minutes to this Year 1673 yet in process of time it alters in some places more than the Variation and in some places near as much as the Variation The Alteration of the Inclination here at London is above Twelve Degrees and therefore very unlikely to find the Latitude by it A Question may be made Whether the Longitude may be found at Sea by the Inclinatory Needle I Answer It may if it be fitted and kept as it ought to be it will do its office as well as the Azimuth-Compass doth to find the Variation Now I shall set down Demonstration of my Son Henry Bond 's Observation at Ballasore in East-India in 1667 which I have before mentioned Fig. III. Example I. At Ballasore forementioned in East-India North Latitude 22 d. 30 m. the Complement P B 67 d. 30 m. and N B 72 d. 33 m. the Distance between the Zenith of Ballasore and the Magnepole and N P 8 d. 30 m. the Distance between the Magnepole and the Pole of the Earth Here we have alwayes three Sides of a Spherical Triangle given to find an Angle which is not hard to do it is no difficult thing to find the Angle at P which is the difference of Longitude between the Magnestical Colure and the Meridian of the place where the Observation is made ☞ We add the three Sides together B N 72 d. 33 m. and the Side B P 67 d. 30 m. and the Side P N 8 d. 30 m. their Sum is 148 d. 33 m. their half Sum 74 d. 16 m ½ from which Substract 8 d. 30 m. one containing Side of the Angle sought the first Difference is 65 d. 46 m. ½ and Substract
between the Earths-Zenith of London and the Magnepole to be 33 d. 19 m. to which the Inclination against it in the Caroline Tables is 71 d. 48 m. which differs but two Minutes from tnat which Robert Norman said it was about viz. 71 d. 50 m. If Robert Norman had set down the Year and the time of the Year when his Observation of the Inclination was made as Mr. Burrowes did of the Variation we should not have differed any thing at all from him the Inclination was then encreasing but now it is decreasing aind will be until the Year 1957 and then the Variation will be nothing at London as it was nothing in 1657 being 300 years distant If we divide the Year into Thirty Six parts we shall find in what time the procession of the Magnesticial Colure goeth forwards one Minute or one Mile of the Equator of the Earth which time will be Ten Dayes Three Hours and Thirty Minutes which being multiplied by 36 tne Product will be 365 Dayes and 6 Hours Having gone thus far to find in what time the Magnesticial Colure goeth forwards one Mile of the Aequator of the Earth if we examine how much it goeth forward in 24 hours it will be 591.37 Foot and in one hour 24.64 Foot here we account one Mile according to Mr. Richard Norwood's Experiment set down in his Sea-man's Practice which is 6000 English Feet to one Mile or Minute of the Aequator or Meridian according to the French 26.39 in one hour and in one Minute 5.278 inches The last thing shall be to find the least and the greatest Inclination of the Inclinatory Needle in any Latitude Substract 8 d. 30 m. from the Complement of the Latitude and look the remainer in the Tables and right against it is the greatest Inclination in that Latitude and add 8 d. 30 m. to the Complement of the Latitude and look the sum in the Tables and right against it is the least Inclination Example 1. Here at London the Complement of the Latitude 38 d. 28 m. and 8 d. 30 m. added together the sum is 46 d. 58. m. against which there is in the Table 61 d. 50 m. the least Inclination And substract 8 d. 30 m. from 38 d. 28 m. and the Remainer is 29 d. 58 m. against which in the Table is 73 d. 55 m. the greatest Inclination here at London which was in the Year 1657. If the Complement of the Latitude and 8 d. 30 m. added together exceed 90 d. 00 m. Substract it out of 180 d. 00 m. and look the remainer in the Table then if the Latitude given be North the least Inclination is of the South end of the Needle But if the Latitude given be South the least Inclination is of the North end of the Needle Example II. In North Latitude 7 d. 00 m. the Complement 83 d. 00 m. unto which 8 d. 30 m. added makes 91 d. 30 m. the remainer to 180 d. 00 m. is 88 d. 30 m. against which in the Table is 3 d. 00 m. the least Inclination of the South end of the Needle the greatest Inclination will be of the North end Then Subtract 8 d. 30 m. from 83 d. 00 m. the complement of the Latitude the remainer is 74 d. 30 m. against which in the Table is 29 d. 00 m. for the greatest Inclination of the North end of the Needle in that Latitude Here is the Conclusion of Thirty Eight Years Magnetick Study and Observations I know when this Mystery comes to be publickly and foreignly known it will be the admiration of all the Christian Nations in the world What then shall any man have high thoughts of himself for it God forbid Far be it from him let him look upon himself as an Instrument in the Hand of Almighty God to declare that which he hath concealed untill his own Time came that he was pleased to make it known for his own Glory and the Benefit of Men in the World Therefore unto Almighty God be all the Praise and Glory of This and all the rest of his Wonderful Works Here follow the CAROLINE TABLES of the Complements of the Magnilatitudes to every Five Minutes of Inclination of the Inclinatory Needle from the Magnequator unto 84 d. 01 m. of Magnilatitude and 87 d. 00 m. of Inclination d. m. d. m. 0 05 89 58 0 10 89 55 0 15 89 53 0 20 89 50 0 25 89 48 0 30 89 45 0 35 89 43 0 40 89 40 0 45 89 38 0 50 89 35 0 55 89 33 1 00 89 30 1 05 89 28 1 10 89 25 1 15 89 23 1 20 89 20 1 25 89 18 1 30 89 15 1 35 89 13 1 40 89 10 1 45 89 08 1 50 89 05 1 55 89 03 2 00 89 00 2 05 88 58 2 10 88 55 2 15 88 53 2 20 88 50 2 25 88 48 2 30 88 45 2 35 88 43 2 40 88 40 2 45 88 38 2 50 88 35 2 55 88 32 3 00 88 30 3 05 88 28 3 10 88 25 3 15 88 22 3 20 88 20 3 25 88 18 3 30 88 15 3 35 88 13 3 40 88 10 3 45 88 08 3 50 88 05 3 55 88 03 4 00 88 00 4 05 87 57 4 10 87 55 4 15 87 53 4 20 87 50 4 25 87 48 4 30 87 45 4 35 87 42 4 40 87 40 4 45 87 37 4 50 87 35 4 55 87 32 5 00 87 30 5 05 87 27 5 10 87 25 5 15 87 22 5 20 87 20 5 25 87 17 5 30 87 15 5 35 87 12 5 40 87 10 5 45 87 07 5 50 87 05 5 55 87 02 6 00 87 00 6 05 86 57 6 10 86 55 6 15 86 52 6 20 86 50 6 25 86 47 6 30 86 45 6 35 86 42 6 40 86 40 6 45 86 37 6 50 86 35 6 55 86 32 7 00 86 29 7 05 86 27 7 10 86 24 7 15 86 21 7 20 86 19 7 25 86 16 7 30 86 14 7 35 86 11 7 40 86 09 7 45 86 06 7 50 86 04 7 55 86 01 8 00 85 59 8 05 85 56 8 10 85 54 8 15 85 51 8 20 85 49 8 25 85 46 8 30 85 44 8 35 85 41 8 40 85 39 8 45 85 36 8 50 85 34 8 55 85 31 9 00 85 29 9 05 85 26 9 10 85 23 9 15 85 20 9 20 85 18 9 25 85 16 9 30 85 13 9 35 85 10 9 40 85 08 9 45 85 05 9 50 85 03 9 55 85 01 10 00 84 58 10 05 84 55 10 10 84 53 10 15 84 50 10 20 84 47 10 25 84 45 10 30 84 42 10 35 84 40 10 40 84 37 10 45 84 35 10 50 84 32 10 55 84 29 11 00 84 27 11 05 84 24 11 10 84 22 11 15 84 19 11 20 84 17 11 25 84 14 11 30 84 12 11 35 84 09 11 40 84 06 11 45 84 04 11
the co-latitude of the place 67 d. 30 m. the other containing Side of the Angle sought from the half Sum and the second Difference is 6 d. 46 m. ½ Then add the Sine of the first Difference 65 d. 46 m. ½ which Sine is 995996 the Sine of the second Difference 6 d. 46 m. ½ which Sine is 907177 and the residuum of the Sine of 67 d. 30 m. which is 083030 and the residum of the Sine of 67 d. 30 m. which is 003438. The whole Sum of the two Sines and the two Residuums is 1989664 the half whereof is 994832 which is the Sine of 62 d. 36 m. half the Difference of Longitude between Ballasore and the Magnestical Colure which being doubled makes 125 d. 12 m. for the whole Difference of Longitude from which substract 6 d. 00 m. the Difference of Longitude between London and the Magnestical Colure in the year 1667. and the Remainer is 119 d. 12 m. the Angle B P V. the Difference of Longitude between London and Ballasore The like is to be done for any place that is on the North side of the Magnequator In the Year 1666 in June the Magnepole was in the Meridian of the Lizard Our Second Example shall be at the Cape of Good Hope in the Year 1666. Which is in South-Latitude 35 d. 30 m. The Inclination of the South end of the Inclinatory Needle at that place is 47 d. 5 m. to which there answers in the Carolina Tables 61 d. 44 m. the Complement of the Magne-latitude or the Distance between the Earth-Zenith of the Cape and the South Magnepole as it appears in the Second Demonstration Wherein let the Circle S L E P O W represent the Magnestical Colure and the Meridian of the Lizard P the North Pole and S the South Pole of the Earth P C S the Meridian of the Cape at C and let N represent the North Magnepole and M the South Magnepole and let the Arch N C M represent the Magnemeridian of the Cape and O R L the Aequator of the Earth and W R E the Magnequator Fig. IIII Our Third Example shall be in 1673 between the Lizard and Cape Charles on the Coast of Virginia In the Demonstration let the Circle S L E P O W represent the Magnesticial Colure N the North Magnepole and M the South P the North Pole of the Earth and S the South W R E the Aequator of the Earth O R L the Magnequator P V S the Meridian of Virginia viz. of Cape Charles N V M the Magnimeridian of Cape Charles and V represent Cape Charles and let the Circle S K Q P F represent the Meridian of the Lizard which is 4 d. 12 m. to the Eastwards of the Magnesticial Colure as it appears in the Demonstration the Inclination of the Needle as is before mentioned is 59 d. 50 m. to which answers in the Caroline Tables 49 d. 18 m. the Distance of the Earths-Zenith of Cape Charles from the North Magnepole the Side N V the co-latitude of Cape Charles 52 d. 20 m. and P N the Distance of the two Poles 8 d. 30 m. The Sum of the three Sides 110 d. 8 m. the half Sum 55 d. 4 m. the first Difference between 8 d. 30 m. and the half Sum is 46 d. 34 m. the second Difference between the co-latitude of Cape Charles and the half Sum is 2 d. 44. m. the Sine of the first Difference 986223. the Sine of the second Difference 867840 the Residuum of 8 d. 30 m. is 083029 the Residuum of the Sine of 52 d. 20 m. 010150. the Sum of them all is 1947244 the half Sum is 97â—622 which is the Sine of â—â— d. 00 m. which being doubled is 66 d. 20 m. unto which if we add 4 d. 12 m. the Difference Fig. V of Longitude that the Magnepole is gone to the Westwards of the Meridian of the Lizard in June 1673 the whole Sum is 70 d. 12 m. the Difference of Longitude between Cape Charles and the Lizard which is according to the Account of Capt. John Whittee who found it in several Voyages to be 70 d. 00 m. little more or less FIG V. Our Fourth Example shall be between the Lizard and the Streights of Magellan in 1673. by Supposition because we have no Observation there but do it according to that which we find to be the truest Longitude and also to shew a Demonstration to know the Longitude of such Places as are to the Westwards and in South-Latitude may be found In the Demonstration let the Circle S E P W represent the Magnesticial Colure S K Q P F represents the Meridian of the Lizard and P B S the North Pole of the Earth and S the South Pole P B S the Meridian of the Streights of Magellan B Ma the Latitude of it 52 d. 20 m. and let N represent the North Magnepole and M the South Magnepole N Ma the Ma M the Magnemeridian of the Streights and Ma the Streight it self The Inclination of the South end of the Inclinatory Needle there 65 d. 26 m. to which answers in the Caroline Tables 42 d. 26 m. the Distance between the Earth-Zenith of the Streights and the South Magnepole viz. Ma M in the Demonstration Here we have three Sides of a Spherical Triangle FIG VI. Ma S the co-latitude of the Streights 37 d. 40 m. and Ma M the Magne-co-latitude of the Streights 42 d. 26 m. and S M the Distance of the two Poles 8 d. 30 m. the Sum of the three sides 88 d. 36 m. the half sum 44 d. 18 m. the first Difference between 8 d. 30 m. and the half sum 35 d. 48 m. the second Difference 6 d. 38 m. between the co-latitude of the Streights and the half sum Fig. VI. Fig. VII For a further Demonstration of this business of Longitude we will find by our Calculation Robert Norman's Inclination that he found in the Year 1576 or else one Year after which Inclination he writes of in the end of the Fourth Chapter of his New Attractive and saith it was about 71 d. 50 m. so are his words now if we go backwards accounting Thirty Six Minutes a Year for the procession of the Magnesticial Colure from the Year 1576 unto the Year 1657 the time will be 81 years which multiplied by 6 10 product will be 48 d. 63 m. the Difference of Longitude between the Magnesticial Colure and the Meridian of London in June 1576 FIG VII I begin the Year in this business when the Sun is in the North Tropick In the Triangle L P M we have the co-latitude of London L P 38 d. 28 m. and the Distance the Magnepole from the Pole of the Earth M P 8 d. 30 m. and the Angle at P 48 d. 36 m. the Difference of Longitude between the Magnesticial Colure and the Meridian of London by which we find the side L M the Distance