The longitude found, or, A treatise shewing an easie and speedy way, as well by night as by day, to find the longitude, having but the latitude of the place and the inclination of the magnetical inclinatorie needle by Henry Bond ...

The LONGITƲDE Found.

WHereas of late dayes there hath been pretending for Longitude, I shall not trou∣ble my self with contradi∣cting any of their wayes, but shew a way which Al∣mighty 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 La∣titude of any place by the Inclination of the Inclinatory Magnetical Needle under the Hori∣zon; 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 Memo∣ries, viz. Dr. Gilbert, Physician in ordinary to Queen Elizabeth, and Mr. Barlow of Win∣chester, 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 La∣titudes) 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 Nee∣dle; and Mr. Edward Wright's Table of Incli∣nations, 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 Naviga∣tion, sets down several Reasons, as he thought, against Magnetical Poles; but I shall make it manifest from Eighty five years Observati∣ons,

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 Kalen∣dar 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 We∣sterly, 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 Cal∣culations to find their Distance from the Poles of the World; but his mind was, that they were, or rather the North Mag∣netick 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 consi∣dered 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 ob∣served 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 Vay∣gats, 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 ap∣pears 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 Longi∣tude 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 inclu∣ded, to find P M, the Distance of the Mag∣netical Pole from the Pole of the Earth, 8 d. 30 m.

The finding of the motion of these Mag∣netical 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. Hen∣ry Gellibrand, the next Professor of Astrono∣my 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? Second∣ly, 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.

For Answer to the Second; Their moti∣on is caused or proceedeth, or may be cau∣sed from the motion of the Earth, and may be as great an Argument of the Earths mo∣tion, as any yet known (if not a greater) the Earths motion being from West to East, and a solid Body; and the Magnetick Sphere

[illustration] Schematic displaying method of locating magnetic poles

Fig. I

that compasseth the Earth, being a Substance that hath not solidity to keep pace with the motion of the Earth, but loseth in its moti∣on; and that may be the cause of the mo∣tion of the Magnetick Poles from East to West; and their motion is the cause of the variating of the variation of the Magnetical Needle, and the cause of the Alteration of the Inclination of the Inclinatory Needle.* 1.1

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 Hun∣dred 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

to October, when Mr. Burrowes did Observe, was Four Months, which took away the Twelve Minutes.

Mr. John Kepler that was Mathematician to the Emperor of Germany, by his Chro∣nology of Time, accounts it from the Cre∣ation of the World, to the Year of our Lord, 1657, to be 5650 years; and this motion of the Magnetick Poles (notwith∣standing it be many times swifter than that motion he accounts upon, yet) gives the same time with his, which makes me much to admire it.

I doubt not but the Learned in Astro∣nomy, will in time collect something more from it (than I have done) or than hath been formerly known.

Their motion is by Sixes, Six Tenths of a Degree in one year, Six Degrees in Ten years, Sixty Degrees in a Hundred years, and Six times Sixty Degrees in Six Hundred years.

I have heard that some Divines in former Dayes have been of opinion, That as the World and all the Creatures were Crea∣ted in Six Dayes, so the World would con∣tinue

Six Thousand Years; but I will not meddle with that. These Magnetick Poles are now in their Tenth Revolution, and as I said before, agree in Time with Kepler's Motion.

They will be in June 1674. Ten Degrees and Twelve Minutes to the Westwards of the Meridian of London, and Four Degrees and Forty Eight Minutes to the Westwards of the Meridian of the Lizard.

The use of the Horizontal Needle is ad∣mirable; yet the motion of it is a forc'd mo∣tion, and not natural; as it appears very plain by Robert Norman a Compass-maker in Ratcliffe, above Ninety Years past, in his New Attractive, who was the first that ever we read or heard of, that found out the Inclinatory motion of the Magnetick Needle, whose Name ought to be remem∣bred for this thing; and Mr. William Bur∣rowes for the Variation of the Compass.

Almighty God was pleased by these two men so to honour our Nation, that the Va∣riation and the Inclination of the Magne∣tick Needle, should be first found in this Nati∣on, above all the Christian Nations in the World.

And now Almighty God is pleased, above Ninety years after them, to make me an Instrument in his Hand, to put it to an use not formerly thought of; that is, to find the Longitude, that as the beginning of it was in this Kingdom, so the conclusion of it should be here, for the Honour of our Gracious King's Majesty, and his King∣doms, unto whom I humbly beseech Al∣mighty God to grant a long, a prosperous, a happy Reign, and Victory over all His Enemies, Amen.

Robert Norman, in his New Attractive••, mentions one Petro de Medina, that in a Book of his concerning Navigation, did hold it for an Absurdity for men to say that the Magnetick Needle had any Variation at all; He said it was an Errour in the misplacing of the Wires: But leaving him and his Er∣rour, I shall shew how Mr. Norman came to find the Inclination of the Inclinatory Nee∣dle, as he himself writes, and how he came to think of such a Needle; he had made a large Horizontal Needle, and bestowed much time and pains in fitting and polish∣ing of it, and had equally poized it on its

Pin, and when he had touch'd it with the Loadstone, and put it on its Pin again, the North end of it inclined so low, that it was not fit for use; he thought to mend it by cutting off some of the end of it, and cut off so much that he spoiled the Nee∣dle; which brought him into a Passion with himself. After his Passion was over, he considered with himself, whether there might not be such a motion of the Needle, and then made one, and found it so; from whence it appears plainly, that the Inclina∣tory motion of the Needle is the Natural motion; and that the Horizontal motion, although it be of admirable use in the world, yet it is a forced motion.

Some years since I saw an Inclinatory Needle of one Doctor Meret's, of the Physi∣cians Colledge in London, which was made by Robert Norman, in 1578, it being out of order, I fitted it for him. The use of the Inclinatory Needle I shall hereafter shew to find the Longitude, which is a use that our former Learned Magnetick Philosophers did not think of in their time, because they knew not the Variating of the Variation.

We are to take notice, that as there is a Magnetick Sphere that hath two Poles, so there are other Circles belonging to it, as to the other Spheres, an Aequator, two Colures, and Parallel Circles to the Aequator. The Aequator, for distinctions sake, I call the Magnequator; the Colure wherein the Poles are, the Magne∣stical Colure; the other, the Magnoctial Colure; the Magnequator doth in a manner represent the Moons Difference, because the Magno∣ctial Intersections with the Aequator of the Earth, have a Retrograde motion, as the Head and Tail of the Dragon hath.

Also the Magnequator doth in a manner re∣present the Ecliptick, having a form of situ∣ation to the Aequator of the Earth, that the Ecliptick hath to the Aequator of the Heavens; the greatest obliquity being but 8 d. 30. m. as appeareth in the first Scheme. As by the Latitude and Declination of a Star in the Heavens; and knowing on which side of the Solstitial Colure it is, the Right Ascension may be exactly Calculated.

So in this, if the Latitude of any Place be given with the Inclination of the Nee∣dle, and on which side of the Magnetical

Solstitial Colure it is, the Longitude of the Place may be found from the Magnetical Co∣lure, and from that the Longitude from any place in the world; as I shall make it ap∣pear by Examples following.

But before I go further, I shall say some∣thing of the Decrease of our Variation here at London, since the time of Mr. William Bur∣rowes's Observations in October 1580, and shall set down, what the Variations have been found then and since, by Observations, and by my Calculation according to the mo∣tion of the Magnetical Poles.

	d. ′ ″		d. ′ ″
In 1580, M. W. Burrowes,	11-15-00	Bond,	11-15-00	East.
In 1622, M. Edm. Gunter,	05-55-37.	Bond,	05-57-00
In 1634, M. H. Gellibrand,	4-03-00.	Bond,	4-01-00
In 1640, Bond & others,	3-06-40.	Bond.	2-59-00

In 1665, Mr. Robert Hooke, the Professor of Geometry in Gresham College in London, with Mr. William Mar, Mr. Richard Short∣grave, and a Gentleman since Deceased, and Henry Bond, Sen. on the 8th. of June, in the King's Majesties Private Garden at White-Hall, observed the Variation, and found it to be 1 d. 22 m. 30 sec. West.

By Bond's Calculation, it was then 1 d. 25 m. 00 sec.

I have set down these both by Observati∣ons, and also by my Calculations, to give the World satisfaction that I do not delude them, to make them think that I know such things, and cannot prove them.

When any that understand themselves, have made trial by exact Observations, and my Calculations, they will acknowledge me to be honest in that which I have writ∣ten.

There is one that puts it out 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 Under∣standing 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 Igno∣ramus.

I am sorry that out Nation is so much dishonoured, to have things of this Nature

[illustration] Schematic showing methods of calculating relation between Earth and various magnetic spheres

Fig. II.

put out in Print, that we are derided by other Nations for them.

As the Horizontal Needle hath a double mo∣tion about the Round Loadstone, or Terrula, so also the Inclinatory Needle hath a double motion about the Earth, as it plainly ap∣peareth in the Diagram following.

Wherein, let A be the Center of the Earth, and B C D the one half of the Mag∣netical 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 mo∣tions, 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 Magne∣tical Pole,* 1.2 there will be continually one mo∣tion

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 conside∣red concerning those Variations of the Ho∣rizontal Needle, that are not according to the situation of the place from the Magne∣tical 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, ex∣cept we will say one piece of the Earth moves from another, which were very ab∣surd.

If the Inclinatory Needle be fitted as it ought to be, to turn Horizontally as the Horizontal Needle doth, it will find an am∣plitude or an Azimuth, as well as the Azi∣muth-Compass, and hath been so used by Capt. John Wood, now Captain of His Maje∣sties 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 ma∣king, that it is not for such an one that will run headlong to make any thing, al∣though 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 In∣clinatory Needle of five inches long, in a Brass Ring, fitted as it ought to be, to ob∣serve with it on the Land; and in the Year 1667, I wrote to him that the In∣clination 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 Va∣riation 7 d. 30 m. by their Azimuth-Com∣pass.

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 Diffe∣rence 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 Observa∣tion 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, notwithstand∣ing it be so long since, and I have for∣gotten 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 Inclina∣tion, 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 Alte∣ration of the Inclination here at London, is above Twelve Degrees, and therefore ve∣ry unlikely to find the Latitude by it.

A Question may be made, Whether the Longitude may be found at Sea by the Incli∣natory 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 Varia∣tion.

Now I shall set down Demonstration

of my Son Henry Bond's Observation at Bal∣lasore in East-India, in 1667, which I have before mentioned.

In which Demonstration let the Circle S E P W represent the Meridian of London, and let the Circle S M L P N O represent the Magnestical Colure, and M the South Magnepole, and N the North Magnepole, and O R L the Magnequator, and let P B S re∣present the Meridian of Ballasore, and N B M the Magnimeridian of Ballasore, and P the North-Pole of the Earth, and S the South-Pole, and let the Angle W P N be 6 d. 00 m. that the Magnepole is gone from the Meridian of London, from 1657, unto 1667, and the Angle B P V 119 d. 12 m. the difference of Longitude between London and Ballasore, unto which if we add the Angle W P N 6 d. 00 m, we have the Angle B P N 125 d. 12 m. the difference of Longitude between Ballasore and the Magnestical Colure. In the Triangle B P N, we have the Side B P, the Co-lati∣tude of Ballasore, 67 d. 30 m. and the Angle B P N 125 d. 12 m. and the Side P N 8 d. 30 m. the distance between the Magnepole and the Pole of the Earth; by which we

[illustration] Schematic locating various magnetic and longitudinal calculations pertaining to Ballafore in East India.

Fig. III.

find the Side B N, the distance between the Zenith of Ballasore and the Magnepole, 72 d. 33 m. which I look in the Caroline Tables or Inclinations, and find the Inclination of the Needle to be right against it, 32 d. 10 m. By this we may see that if we have the Incli∣nation of the Needle at any place, and know on which side of the Magnestical Colure it is, we may find the Longitude of the place from the Magnestical Colure, and then knowing the motion of the Magnepole, we may find the Longitude of the Magnepole from the Meridian of London, or the Lizard, or from any other Meridian; and so by that find the Difference of Longitude between any two places in the world; as I shall make it ap∣pear by the Examples following; and first Ballasore, as in the following Scheme.* 1.3

Example I.

At Ballasore (forementioned) in East-India, North Latitude, 22 d. 30 m. the Com∣plement P B 67 d. 30 m. and N B 72 d. 33 m. the Distance between the Zenith of Balla∣sore, 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.

* 1.4We 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 con∣taining Side of the Angle sought, the first Difference is 65 d. 46 m. ½; and Substract 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 Diffe∣rence 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 Magne∣pole 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 Ta∣bles 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 De∣monstration.

Wherein, let the Circle S L E P O W, represent the Magnestical Colure, and the Me∣ridian 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 re∣present 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.

In the Triangle C S M, we have the three Sides given, C S 54 d. 30 m. the co-latitude of the Cape, and S M 8 d. 30 m. the Di∣stance of the Pole of the Earth and the Magnepole, and C M 61 d. 44 m. the Di∣stance between the Earth-Zenith of the Cape, and the South Magnepole; the Sum of all the tree Sides is 124 d. 44 m. the half Sum is 62 d. 22 m. From which each con∣taining Side of the Angle required at S, be∣ing substracted, the first Difference is 53 d. 52 m. the second Difference is 7 d. 52 m. the

[illustration] Schematic representing the magnestical colure and the meridian of the Lizard, relating to the Cape of Good Hope in 1666.

Fig. IIII

Sine of the first Difference, 990722. The Sine of the second Difference, 913630. The Residuum of 8 d. 30 m. is 083053. The Re∣siduum of 54 d. 30 m. 008931. The whole Sum of them is 1996336; the half Sum is 998168, which is the Sine of 73 d. 29 m. which being doubled, is 146 d. 58 m. for the Angle C S M; which being substracted from 180 d. 00 m. leaves the Angle V S C, the Longitude of the Cape of Good Hope from the Lizard, whose Meridian was the same with the Magnesticial Coloure in the Year 1666, and their Difference of Longitude is 33 d. 02 m.* 1.5

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 Co∣lure; 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 Dif∣ference 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 Re∣siduum of the Sine of 52 d. 20 m. 010150. the Sum of them all is 1947244, the half Sum is 97••622, which is the Sine of •••• d. 00 m. which being doubled, is 66 d. 20 m. unto which, if we add 4 d. 12 m. the Dif∣ference

[illustration] Schematic displaying various magnetic and longitudinal calculations relating to the Lizard and the Streights of Magellan in 1673.

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 ac∣cording to the Account of Capt. John Whittee, who found it in several Voyages to be 70 d. 00 m. little more or less.* 1.6

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 Lati∣tude of it 52 d. 20 m. and let N represent the North Magnepole, and M the South Ma∣gnepole,

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,* 1.7 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 Di∣stance 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 se∣cond Difference 6 d. 38 m. between the co-latitude of the Streights and the half sum.

The sine of the first Difference, 976712, the sine of the second Difference, 906263, the Residuum of the sine of the co-latitude of the Streights, 021392, the Residuum of the sine of 8 d. 30 m. is 083029, the sum of the four is 1987396, the half sum 993698, which is the sine of 59 d. 52 m. which be∣ing doubled, is 119 d. 44 m. the Angle Ma,

[illustration] Schematic relating to various magnetic and longitudinal calculations around the Streights of Magellan.

Fig. VI.

[illustration] Schematic displaying difference of longitude between the magnesticial colure and the Meridian of London in June 1576

Fig. VII.

S M, which being substracted from 180 d. 00 m, leaves the Angle Ma, S L, the Lon∣gitude of the Streights from the Magnesticial Colure 60 d. 16 m. unto which, if we add the Angle N P Q, the Difference of Longi∣tude that the Magnesticial Colure is to the Westward of the Lizard in June 1673, the sum is 64 d. 28 m. the Longitude of the Streights of Magellan from the Lizard.

For a further Demonstration of this bu∣siness 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,* 1.8 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 Di∣stance 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 be∣tween the Magnesticial Colure and the Meri∣dian of London; by which we find the side L M (the Distance between the Earths-Ze∣nith 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 dif∣fers 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 Obser∣vation 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 pro∣cession of the Magnesticial Colure goeth for∣wards

one Minute, or one Mile of the Equa∣tor 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 Ex∣periment set down in his Sea-man's Practice, which is 6000 English Feet to one Mile or Minute of the Aequator or Meridian, accor∣ding 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 Nee∣dle 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 grea∣test Inclination in that Latitude, and add

8 d. 30 m. to the Complement of the Lati∣tude, 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 grea∣test 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 La∣titude given be North, the least Inclination is of the South end of the Needle: But if the Latitude given be South, the least In∣clination is of the North end of the Nee∣dle.

Example II.

In North Latitude 7 d. 00 m. the Comple∣ment, 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 re∣mainer is 74 d. 30 m. against which in the Table is 29 d. 00 m. for the greatest Incli∣nation 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 Be∣nefit 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.

Notes

• * 1.1

  FIG. I.
• * 1.2

  FIG. II.
• * 1.3

  FIG. III
• * 1.4

  ☞
• * 1.5

  FIG. IV.
• * 1.6

  FIG. V.
• * 1.7

  FIG. VI.
• * 1.8

  FIG. VII.