Decameron physiologicum, or, Ten dialogues of natural philosophy by Thomas Hobbes ... ; to which is added The proportion of a straight line to half the arc of a quadrant, by the same author.

CAP. IX. Of the Loadstone, and its Poles; and whether they shew the Longitude of places on the Earth. (Book 9)

A.

I Come now to hear what Natural Causes you can assign of the vertues of the Magnet; and first, why it draws Iron to it, and only Iron.

B.

You know I have no other cause to assign but some local Motion, and that I never ap∣proved of any argument drawn from Sympa∣thy, Influence, Substantial Forms, or Incorpo∣real Effluvia. For I am not, nor am accounted by my Antagonists for a Witch. But to an∣swer this Question, I should describe the Globe of the Earth greater than it is at B in the first Figure, but that the Terrella in the fourth Fi∣gure will serve our turn. For 'tis but calling B and C the Poles of the Earth, and D E the Diameter of the Aequinoctial Circle, and making D the East, and E the West. And

then you must remember that the Annual Motion of the Earth is from West to East, and compounded of a straight and circular Motion, so as that every point of it shall describe a small Circle from West to East, as is done by the whole Globe. And let the Circles about a b c be three of those small Circles.

A.

Before you go any further, I pray you shew me how I must distinguish East and West in every part of this Figure. For wheresoever I am on Earth (suppose at London) and see the Sun rise (suppose in Cancer) is not a straight line from my Eye to the Sun termi∣nated in the East?

B.

'Tis not due East, but partly East, partly South. For the Earth (being but a point compared to the Sun) all the parallels to D E the Aequator, such as are e a, f b, e g, if they be produced, will fall upon the Body of the Sun. And therefore A b is North-East; A a East North-East; And A c North North-East.

A.

Proceed now to the Cause of Attraction.

B.

Suppose now that the Internal parts of the Loadstone had the same Motion with that of the Internal parts of the Sun which make the Annual Motion of the Earth from West to East, but in a contrary way, for otherwise the Loadstone and the Iron can never be made to meet. Then set the Loadstone at a little distance from the Earth, marked with z; and

the Iron marked with x upon the superficies of the Earth. Now that which makes x rise to z, can be nothing else but Air; for no∣thing touches it but Air. And that which makes the Air to rise, can be nothing but those small circles made by the parts of the Earth (such as are at a b c,) for nothing else touches the Air. Seeing then the Motion of each point of the Loadstone is from East to West in Circles, and the motion of each point of the Iron from West to East; it follows, that the Air between the Loadstone and the Iron shall be cast off both East and West; and con∣sequently the place left empty, if the Iron did not rise up and fill it. Thus you see the Cause that maketh the Loadstone and the Iron to meet.

A.

Hitherto I assent. But why they should meet when some Heterogeneous Body lyes in the Air between them, I cannot imagine. And yet I have seen a Knife, though within the Sheath, attract one end of the Needle of a Mariners Compass; and have heard it will do the same though a Stone-wall were be∣tween.

B.

Such Iron were indeed a very and vi∣gorous Loadstone. But the Cause of it is the same that causeth Fire or hot Water (which have the same compounded Motion) to work through a Vessel of Brass. For though the Motion be altered by restraint within the

Heterogeneous Body, yet being continued quite through it restores it self.

A.

What is the Cause why the Iron rub'd over by a Loadstone will receive the vertue which the Loadstone hath of drawing Iron to it?

B.

Since the Motion that brings two Bodies to meet must have contrary ways, and that the Motions of the Internal parts of the Mag∣net and of the Iron are contrary; the rubbing of them together does not give the Iron the first Edeavour to rise, but multiplies it. For the Iron untouch'd will rise to a Loadstone; but if touch'd, it becomes a Loadstone to other Iron. For when they touch a piece of Iron they pass the Loadstone over it only one way, viz. from Pole to Pole; not back again, for that would undo what before had been done; also they press it in passing, to the very end of the Iron, and somewhat hard. So that by this pressing Motion all the small Circles about the points a b c, are turned the contrary way. And the halves of those small Circles made on the Arch D B will be taken away, and the Poles changed, so as that the North-Poles shall point South, and the South Poles North, as in the Figure.

A.

But how comes it to pass, that when a Loadstone hath drawn a piece of Iron, you may add to it another, as if they begat one another? Is there the like Motion in the ge∣neration of Animals?

B.

I have told you that Iron of it self will rise to the Loadstone. Much more then will it adhere to it when it is armed with Iron, and both it and the Iron have a plain Super∣ficies. For then not only the points of Con∣tact will be many (which make the coherence stronger) but also the Iron wherewith it is armed is now another Loadstone, differing a little (which you perhaps think) as Male and Female. But whether this compounded Mo∣tion and confrication causeth the generation of Animals, how should I know, that never had so much leasure as to make any observa∣tion which might conduce to that?

A.

My next Question is, seeing you say the Loadstone, or a Needle touch'd with it, na∣turally respecteth the Poles of the Earth, but that the variation of it proceedeth from some accidents in the Superficies of the Earth; what are those accidents?

B.

Suppose there be a Hill upon the Earth (for example) at r; then the stream of the Air which was between z and x Westward, coming to the Hill, shall go up the Hills side, and so down to the other side, according to the crooked Line which I have mark'd about the Hill by points; and this infallibly will turn the North-point of the Needle, being on the East side, more toward the East, and that on the other side more towards the West, than if there had been no Hill. And where

upon the Earth are there not Eminencies and depressions, except in some wide Sea, and a great way from Land?

A.

But if that be true, the Variation in the same place should be always the same. For the Hills are not removed.

B.

The Variation of the Needle at the same place is still the same: but the Variation of the Variation is partly from the Motion of the Pole it self, which by the Astronomers is cal∣led Motus trepidationis; and partly from that, that the Variation cannot be truly observ'd: for the Horizontal Needle and the Inclina∣tory Needle incline alike, but cannot incline in due quantity. For whether set upon a Pin or an Axis, their Inclination is hindred in the Horizontal Needle by the Pin it self. If upon an Axis, if the Axis be just, it cannot move; if slack, the weight will hinder it. But chief∣ly because the North Pole of the Earth draws away from it the North Pole of the Needle. For two like Poles cannot come together. And this is the cause why the Variation in one place is East, and another West.

A.

This is indeed the most probable reason why the Variation varies, that ever I heard given. And I should presently acknowledge that this parallel Motion of the Axis of the Earth in the Ecliptick, supposed by Coper∣nicus, is the true Annual Motion of the Earth, but that there is lately come forth a Book

called Longitude found, which makes the Magnetical Poles distant from the Poles of the Earth eight Degrees and a half.

B.

I have the Book. 'Tis far from being demonstrated, as you shall find if you have the patience to see it examined. For where∣soever his demonstration is true, the conclu∣sion (if rightly inferred) will be this, that the Poles of the Loadstone and the Poles of the Earth are the same. And where on the con∣trary his demonstrations are fallacies, it is be∣cause sometimes he fancieth the Lines he hath drawn, not where they are; sometimes be∣cause he mistakes his station; and sometimes because he goes on some false Principle of Natural Philosophy; and sometimes also be∣cause he knoweth not sufficiently the Doctrine of Spherical Triangles.

A.

I think that's the Book there which lyes at your Elbow. Pray you read.

B.

I find first (Pag. 4.) that the ground of his Argument are the two observations made by Mr. Burroughs; one at Vaygates, in 1676, where the Variation from the Pole of the Earth he found to be 11 deg. 15 min. East; the other at Lime-house near London, in 1580, where the Variation from the Pole of the Earth was 8 deg. 38 min. West. By which he saith, he might find out the Magnetical Pole.

A.

Where is Vaygate?

B.

In 70 Degrees of North Latitude, the difference of Longitude between London and it being 58 Degrees.

A.

The Longitude of places being yet to seek, how came he to know this difference of 58 Degrees, except the Poles of the Magnet and the Earth be the same?

B.

I believe he trusted to the Globe for that. For the distance between the places is not above 2000 Miles the nearest way. But we will pass by that, and come to his Demon∣stration, and to his Diagram, wherein L is London, P the North-Pole of the Earth, V Vaygates. So that L P is 38 deg. 28 min. P V 20 deg. the Angle L P V 58 deg. for the difference between the Longitudes of Vaygates and London. This is the Constru∣ction. But before I come to the demonstra∣tion, I have an Inference to draw from these observations, which is this. Because in the same year the Variation at London was 11 deg. 15 min. East, and at Vaygates 8 deg. 38 min. West; If you substract 11 deg. 15 min. from the Arc L P; and 8 deg. 38 min. from the Arc L V, the Variation on both sides will be taken away; so that P V being the Meridian of Vaygates, and L P the Meri∣dian of London, they shall both of them meet in P the Pole of the Earth. And if the Pole of the Magnet be nearer to the Zenith of London than is the Pole of the Earth, it shall

be just as much nearer to the Zenith of Vay∣gates in the Meridian of Vaygates which is P V; as is manifest by the Diurnal Motion of the Earth.

A.

All this I conceive without difficulty. Proceed to the Demonstration.

B.

Mark well now. His words are these, (Pag. 5.) From P L V substract 11 deg. 15 min. and there remains the Angle V L M. Consi∣der now which is the Angle P L V, and which is the remaining Angle V L M, and tell what you understand by it.

A.

He has mark'd the Angle P L V with two numbers, 11 deg. 15 min. and 21 deg. 50 min. which together make 33 deg. 5 min. And the Angle 11 deg. 15 min. being sub∣stracted from P L V, there will remain 21 deg. 50 min. for the Angle V L M. I know not what to say to it. For I thought the Arc P V, which is 20 deg. had been the Arc of the Spherical Angle P L V; and that the Arc L V had been 58 deg. because he says the Angle L P V is so; and that the Arc L M had been 46 deg. because the Angle L P M is so; and lastly, that the Angle P L M had been 8 deg. 30 min. because the Arc P M is so.

B.

And what you thought had been true, if a Spherical Angle were a very Angle. For all Men that have written of Spherical Tri∣angles take for the ground of their calculation (as Regiomontanus, Copernicus, and Clavius,)

that the Arch of a Spherical Angle is the side opposite to the Angle. You should have con∣sidered also that he makes the Angle V P M 12 deg. but sets down no Arc to answer it. But that you may find I am in the right, look into the Definitions which Clavius hath put down before his Treatise of Spherical Tri∣angles, and amongst them is this; The Arc of a Spherical Triangle is a part of a great Circle intercepted between the two sides drawn from the Pole of the said great Circle.

A.

The Book is nothing worth; for it is impossible to substract an Arc of a Circle out of a Spherical Angle. And I see besides that he takes the Superficies that lyeth between the sides L P and L M for an Arch, which is the quantity of an Angle; and is a Line, and can∣not be taken out of a Superficies. I wonder how any Man that pretends to Mathematicks could be so much mistaken.

B.

'Tis no great wonder. For Clavius him∣self striving to maintain that a right Angle is greater than the Angle made by the Diameter and the Circumference, fell into the same errour. A corner (in Vulgar Speech,) and an Angle (in the Language of Geometry) are not the same thing. But it is easie even for a learned Man sometimes to take them for the same, as this Author now has done; and proceeding he saith, Substract 8 deg. 38 min. from the Angle P V L, and there remains the Angle L V M.

A.

That again is false, because impossible. What was it that deceiv'd him now?

B.

The same misunderstanding of the na∣ture of a Spherical Angle. Which appears further in this, that when he knew the Arc V P was part of a great Circle, he thought V M (which he maketh 8 deg. 30 min.) were also parts of a great Circle; which is mani∣festly false. For two great Circles (because they pass through the Center) do cut each other into halves. But P V is not half a Circle. He sure thought himself at Vaygates, and that P M V was equal to P V, although in the same Hemisphere.

A.

But how proves he that the Arc PM is 8 deg. 30 min?

B.

Thus. We have in two Triangles, P L M 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 deg. 30 min.

A.

Is that all? 'Tis very short for a Demon∣stration of two so difficult Problems, as the quantity of 8 deg. 30 min. and of the place of the Magnetical Pole. But he has proved no∣thing till he has shew'd how he found it. And though P M be 8 deg. 30 min. it follows not that M is the Magnetical Pole.

B.

Nor is it true. For if P M be 8 deg. 30 min. and V M 8 deg. 38 min. the whole Arc P M V will be 17 deg. 8 min. which should be 20 deg. Besides, whereas the Varia∣tions

were East and West, the substracting of them should be also East and West, but they are North and South.

A.

I am satisfied that the Magnetical Poles and the Poles of the Earth are the same. But thus much I confess, that if they were not the same, the Longitude were found. For the difference of the Latitudes of the Earths Aequator and of the Magnetical Aequator is the difference of the Longitude. But proceed.

B.

The Earth being a solid Body, and the Magnetick Sphere that encompasseth the Earth being a substance that hath not solidity to keep pace with the Earth, looseth in its Motion. And that may be the Cause of the Motion of the Magnetick Poles from East to West.

A.

This is very fine, and unexpected. The Magnetick Sphere (which I took for a Globe made of a Magnet) has not solidity to keep pace with the Earth, though it be one of the hardest Stones that are. It encompasseth the Earth; yet I thought nothing had encompas∣sed the Earth but Air in which I breath and move. By this also the whole Earth must be a Loadstone. For two Bodies cannot be in one place. So that he is yet no further than Dr. Gilbert whom he sleights. And if the Sphere be a Magnet, then the Earth and Load∣stone have the same Poles. See the force of Truth! which though it could not draw to it his reason, hath drawn his words to it.

B.

But perhaps he meant that the Magne∣tick vertue encompasseth the Earth, and not the Magnetick Body.

A.

But that helpeth him not. For if the Body of the Magnet be not there, the vertue then is the vertue of the Earth; and so again the Poles of the Earth are Magnetick Poles.

B.

You see how unsafe it is to boast of Doctrines as of Gods gifts, till we are sure that they are true. For God giveth and denieth as he pleaseth, not as our selves wish; as now to him he hath given Confidence enough, but hath denied him (at least hitherto) the find∣ing of the Longitudes. In the next place (Pag. 8.) he seems much pleased that his Doctrine agrees with an opinion of Keplerus, That from the Creation to the year of our Lord it is to the year 1657 now 5650 years; and with that which he saith some Divines have held in times past, That as this World was created in six days, so it should continue six thousand years. By which account the World will be at an end 350 years hence; though the Scripture tell us it shall come as a Thief in the night. O what advantage 340 years hence will they have that know this, over them that know it not, by taking up Money at Interest, or selling Lands at 20 years purchase!

A.

But he says he will not meddle with that.

B.

Yes, when he had medled with it too much already.

A.

But you have not told me wherein con∣sisteth this Agreement between him and Ke∣plerus.

B.

I forgot it. 'Tis in the Motion of the Magnetick Poles. For precedently (Pag. 7.) he had said that their Period or Revolution was 600 years; their yearly Motion 36 min. and (Pag. 8.) that their Motion is by sixes. Six tenths of a degree in one year; six degrees in ten year; sixty degrees in a hundred year; and six times sixty degrees in 600 year.

A.

But what Natural Cause doth he assign of this revolution of 600 years?

B.

None at all. For the Magnet lying upon the Earth, can have no Motion at all but what the Earth and the Air give it. And because it is always at 8 deg. 30 min. distance from the Pole of the Earth, the Earth can give it no other Motion than what it gives to its own Poles by the precession of the Aequinoctial points. Nor can the Air give it any Motion but by its Stream; which must needs vary when the Stream varieth. But what a vast difference does he make between the period of the Motion of the Aequinoctial points, which are about or near 36000 years accor∣ding to Copernicus (Lib. 3. Cap. 6.) which makes the Annual precession to be 36 seconds, and the period of the Magnetical Poles Mo∣tion, which is but 600 years.

A.

Go on.

B.

He comes now (Pag. 15.) to the Incli∣natory Needle upon a Spherical Loadstone. Where he shews, by Diagram, that the Needle and the Instrument together moved toward the Magnetical Pole, make the sum of the In∣clinations equal to two Quadrants, setting the North-point of the Needle Southward. Which I confess is true. But (in the same Page) he ascribeth the same Motion to the Earth in these words: As the Horizontal Needle hath a double Motion about the Round Load∣stone or Terrulla, so also the Inclinatory Needle hath a double Motion about the Earth. What is this, but a confession that the Poles of the Magnet and of the Earth are the same?

A.

'Tis plain enough.

B.

Besides, seeing he placeth the Magne∣tical Pole at M in the Meridian of Vaygates, the Needle being touch'd shall Incline to the Pole of the Earth which is P, as well there as at London, and make the North-Pole of the Earth point South.

A.

'Tis certain, because he puts both the Magnetical Pole and the Pole of the Earth in the same Meridian of the Earth. Nor see I any Cause why, the Needle being the same, it should not be as subject to Variation, and to Variation of Variation, and to all Accidents of the Earth there, as in any other part.

B.

He putteth (Pag. 16.) a Question, At what distance from the Earth are the Magne∣tick

Poles? and answers to it, They are very near the Earth, because the nearer the Earth, the greater the strength. What think you of this?

A.

I think they are in the Superficies of the Magnet, as the Pole of the Earth is in the Su∣perficies of the Earth. And consequently, that then the Earth must be a part of the Mag∣net, and their Poles the same. For the Body of the Magnet and the Body of the Earth, if they be two, cannot be in one place.

B.

His next words are, Some things are to be considered concerning those Variations of the Horizontal Needle which are not according to the scituation of the place from the Magne∣tick Poles, but are contrary; as all the West-Indies according to the Poles should be Easterly, and they are Westerly. Which is by some Ac∣cidental Cause in the Earth; and their Motion, as I formerly said, is a forced Motion, and not Natural.

A.

He has clearly overthrown his main Doctrine. For to say the Motion of the Needle is forced and unnatural, is a most pity∣ful shift, and manifestly false, no Motion be∣ing more constant or less accidental, notwith∣standing the Variation, to which the Inclina∣tory Needle is no less subject than the Hori∣zontal Needle.

B.

That which deceived him, was, that he thought them two sorts of Needles, forgetting

what he had said of Normans Invention of the Inclinatory Needle by the inclining of the Horizontal Needle, Pag. 11. For I will shew you that what he says is Easterly and should be Westerly, should be Easterly as it is. Con∣sider the fourth Figure, in which B is the North-Pole, and B c 11 deg. 15 min. Easter∣ly, which was the Variation at London in 1576 Easterly. Suppose A c to be the Needle, shall it not incline, as well here as at D a, and the Variation B c be Easterly? Again, D a is 11 deg. 15 min. and the Needle in D parallel to A B, and at a inclining also 11 deg. 15 min. Westerly. And is not the Variation there D a Westerly, with the North-point of the Needle in the Line a h?

A.

But the West-Indies are not in this He∣misphere B C D E. The Variation therefore will proceed in an Arc of the opposite Hemi∣sphere, which is Westerly.

B.

I believe he might think so, forgetting that he and his Compass were on the Super∣ficies of the Earth, and fancying them in the Center at A.

A.

'Tis like enough. If we had a straight Line exactly equal to the Arc of a Quadrant, I think it would very much facilitate the Do∣ctrine of Spherical Triangles.

B.

When you have done with your Que∣stions of Natural Philosophy, I will give you a clear Demonstration of the equality of a

straight Line to the Arc of a Quadrant, which, if it satisfie you, you may carry with you, and try thereby if you can find the Angle of a Spherical Triangle given.

A.

It is time now to give over. And at our next meeting I desire your opinion con∣cerning the Causes of Diaphaniety, and Re∣fraction. This Copernicus has done much more than he thought of. For he has not on∣ly restored to us Astronomy, but also made the way open to Physiology.