OF THE LOADSTONE AND ITS POLES, AND WHETHER
THEY SHOW THE LONGITUDE OF PLACES ON THE EARTH.
_A._ I come now to hear what natural causes you can assign of the
virtues 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 approved of any argument drawn from sympathy, influence,
substantial forms, or incorporeal effluvia. For I am not, nor am
accounted by my antagonists for a witch. But to answer 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 figure will serve our
turn. For it is but calling B and C the poles of the earth, and D E the
diameter of the equinoctial 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 farther, I pray you show 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 terminated in the
east?
_B._ It is 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
equator, such as are _e a_, _f b_, _c 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 nothing
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 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 consequently 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 lies 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
mariner’s compass; and have heard it will do the same though a
stone-wall were between.
_B._ Such iron were indeed a very vigorous 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 itself.
_A._ What is the cause why the iron rubbed over by a loadstone will
receive the virtue 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 magnet and of
the iron are contrary; the rubbing of them together does not give the
iron the first endeavour to rise, but multiplies it. For the iron
untouched will rise to a loadstone; but if touched, 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 generation of animals?
_B._ I have told you that iron of itself 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 superficies. For then not only the points
of contact 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
motion and confrication causeth the generation of animals, how should I
know, that never had so much leisure as to make any observation which
might conduce to that?
_A._ My next question is, seeing you say the loadstone, or a needle
touched with it, naturally 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 hill’s side, and so down to the other side,
according to the crooked line which I have marked about the hill by
points; and this infallibly will turn the north point of the needle,
being on the east side, more towards 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 eminences 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
itself, which by the astronomers is called _motus trepidationis_; and
partly from that, that the variation cannot be truly observed, for the
horizontal needle and the inclinatory needle incline alike, but cannot
incline in due quantity. For whether set upon a pin or an axis, their
inclination is hindered, in the horizontal needle, by the pin itself: if
upon an axis, if the axis be just, it cannot move; if slack, the weight
will hinder it; but chiefly 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 ecliptic, supposed by
Copernicus, 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. It is far from being demonstrated, as you shall
find, if you have the patience to see it examined. For wheresoever his
demonstration is true, the conclusion, 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 contrary, his demonstrations are fallacies, it
is because sometimes he fancieth the lines he hath drawn, not where they
are; sometimes because he mistakes his station; and sometimes because he
goes on some false principle of natural philosophy; and sometimes also
because he knoweth not sufficiently the doctrine of spherical triangles.
_A._ I think that is the book there which lies at your elbow. Pray you
read.
_B._ I find first (p. 4), that the grounds of his argument are the two
observations made by Mr. Burroughs, one at Vaygates, in 1576, where the
variation from the pole of the earth he found to be 11 deg. 15 min.
east; the other at Limehouse, 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 Vaygates?
_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 demonstration, 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 construction.
But before I come to the demonstration, 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 subtract 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 meridian
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
Vaygates 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 (page 5): From P L V subtract 11
deg. 15 min., and there remains the angle V L M. Consider 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 marked 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 subtracted 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 triangles 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 considered 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 triangles, 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 subtract an arc
of a circle out of a spherical angle. And I see besides that he takes
the superficies that lieth between the sides L P and L M for an arch,
which is the quantity of an angle; and is a line, and cannot be taken
out of a superficies. I wonder how any man that pretends to mathematics
could be so much mistaken.
_B._ It is no great wonder. For Clavius himself striving to maintain
that a right angle is greater than the angle made by the diameter and
the circumference, fell into the same error. A corner, in vulgar speech,
and an angle, in the language of geometry, are not the same thing. But
it is easy even for a learned man sometimes to take them for the same,
as this author now has done; and proceeding he saith, subtract 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 deceived
him now?
_B._ The same misunderstanding of the nature of a spherical angle. Which
appears farther 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 manifestly false. For two great
circles, because they pass through the centre, do cut each other into
halves. But V P 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 P M is 8 degrees 30 minutes?
_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? It is very short for a demonstration 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 nothing till he has showed 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 variations were east and west, the subtracting
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, if they were not the same, the
longitude were found. For the difference of the latitudes of the earth’s
equator and of the magnetical equator, is the difference of the
longitude. But proceed.
_B._ “The earth being a solid body, and the magnetic sphere that
encompasseth the earth being a substance that hath not solidity to keep
pace with the earth, loseth in its motion: and that may be the cause of
the motion of the magnetic poles from east to west.”
_A._ This is very fine and unexpected. The magnetic 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 encompassed 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
farther than Dr. Gilbert whom he slights. And if the sphere be a magnet,
then the earth and loadstone 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 magnetic virtue encompasseth the
earth, and not the magnetic body.
_A._ But that helpeth him not. For if the body of the magnet be not
there, the virtue then is the virtue of the earth; and so again the
poles of the earth are magnetic poles.
_B._ You see how unsafe it is to boast of doctrines as of God’s gifts,
till we are sure that they are true. For God giveth and denieth as he
pleaseth, not as ourselves wish; as now to him he hath given confidence
enough, but hath denied him, at least hitherto, the finding of the
longitudes. In the next place (p. 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 three hundred and fifty
years hence; though the Scripture tells us it shall come as a thief in
the night. O what advantage three hundred and forty years hence will
they have that know this, over them that know it not, by taking up money
at interest, or selling lands at twenty years’ purchase!
_A._ But he says he will not meddle with that.
_B._ Yes, when he had meddled with it too much already.
_A._ But you have not told me wherein consisteth this agreement between
him and Keplerus.
_B._ I forgot it. It is in the motion of the magnetic poles. For
precedently (p. 7), he had said “that their period or revolution was six
hundred years; their yearly motion thirty-six minutes; and (p. 8) that
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.”
_A._ But what natural cause doth he assign of this revolution of six
hundred 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 equinoctial 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 equinoctial points, which is about or near thirty-six thousand years
according to Copernicus (lib. iii. cap. 6), which makes the annual
precession to be 36 seconds, and the period of the magnetical poles’
motion, which is but six hundred years.
_A_. Go on.
_B_. He comes now (p. 15) to the inclinatory needle upon a spherical
loadstone. Where he shows, by diagram, that the needle and the
instrument together moved towards the magnetical pole, make the sum of
the inclinations 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 loadstone or
terrella, 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._ It is plain enough.
_B._ Besides, seeing he placeth the magnetical pole at M in the meridian
of Vaygates, the needle being touched 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._ It is 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 (p. 16) a question, “at what distance from the earth are
the magnetic 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 superficies of the earth. And consequently, that
then the earth must be a part of the magnet, 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
situation of the place from the magnetic poles, but are contrary; as all
the West Indies according to the poles should be easterly, and they are
westerly. Which is by some accidental 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 pitiful shift, and
manifestly false, no motion being more constant or less accidental,
notwithstanding the variation, to which the inclinatory needle is no
less subject than the horizontal needle.
_B._ That which deceived him, was, that he thought them two sorts of
needles, forgetting what he had said of Norman’s invention of the
inclinatory needle by the inclining of the horizontal needle (p. 11).
For I will show you that what he says is easterly and should be
westerly, should be easterly as it is. Consider the fourth figure, in
which B is the north-pole, and B _c_ 11 deg. 15 min. easterly, 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 hemisphere B C D E. The
variation therefore will proceed in an arc of the opposite hemisphere,
which is westerly.
_B._ I believe he might think so, forgetting that he and his compass
were on the superficies of the earth, and fancying them in the centre at
A.
_A._ It is like enough. If we had a straight line exactly equal to the
arc of a quadrant, I think it would very much facilitate the doctrine of
spherical triangles.
_B._ When you have done with your questions 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 satisfy 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 concerning the causes of diaphaniety, and refraction. This
Copernicus has done much more than he thought of. For he has not only
restored to us astronomy, but also made the way open to physiology.
==========