OF THE SYSTEM OF THE WORLD.
_B._ You are come in good time; let us therefore sit down. There is ink,
paper, ruler, and compass. Draw a little circle to represent the body of
the sun.
_A._ It is done. The centre is A, the circumference is L M.
_B._ Upon the same centre A, draw a larger circle to stand for the
ecliptic: for you know the sun is always in the plane of the ecliptic.
_A._ There it is. The diameters of it at right angles are B Z.
_B._ Draw the diameter of the equator.
_A._ How?
_B._ Through the centre A (for the earth is also always in the plane of
the equator or of some of its parallels) so as to be distant from B
twenty-three degrees and a half.
_A._ Let it be H I: and let C G be equal to B H; and so C will be one of
the poles of the ecliptic, suppose the north-pole; and then H will be
east, and I west. And C A produced to the circumference in E, makes E
the south-pole.
_B._ Take C K equal to C G, and the chord G K will be the diameter of
the arctic circle, and parallel to H I, the diameter of the equator.
Lastly, upon the point B, draw a little circle wherein I suppose to be
the globe of the earth.
_A._ It is drawn, and marked with _l m_. And B D and K G joined will be
parallel; and as H and I are east and west, and so are B and D, and G
and K.
_B._ True; but producing Z B to the circumference _l m_ in _b_, the line
B _b_ will be in the diameter of the ecliptic of the earth, and B _m_ in
the diameter of the equator of the earth. In like manner, if you produce
K G cutting the circle, whose centre is G, in _d_ and _e_, and make an
angle _n_ G _d_ equal to _b_ B _m_, the line _n_ G will be in the
ecliptic of the earth, because G _d_ is in the equator of the earth. So
that in the annual motion of the earth through the ecliptic, every
straight line drawn in the earth, is perpetually kept parallel to the
place from whence it is removed.
_A._ It is true; and it is the doctrine of Copernicus. But I cannot yet
conceive by what one motion this circle can be described otherwise than
we are taught by Euclid. And then I am sure that all the diameters shall
cross one another in the centre, which in this figure is A.
_B._ I do not say that the diameters of a sphere or circle can be
parallel; but that if a circle of a lesser sphere be moved upon the
circumference of a great circle of a greater sphere, that the straight
lines that are in the lesser sphere may be kept parallel perpetually to
the places they proceed from.
_A._ How? And by what motion?
_B._ Take into your hand any straight line (as in this figure), the line
L A M, which we suppose to be the diameter of the sun’s body; and moving
it parallelly with the ends in the circumference, so as that the end M
may withal describe a small circle, as M _a_. It is manifest that all
the other points of the same line L M will, by the same motion, at the
same time, describe equal circles to it. Likewise if you take in your
hand any two diameters fastened together, the same parallel motion of
the line L M, shall cause all the points of the other diameter to make
equal circles to the same M _a_.
_A._ It is evident; as also that every point of the sun’s body shall do
the like. And not only so, but also if one end describe any other
figure, all the other points of the body shall describe like and equal
figures to it.
_B._ You see by this, that this parallel motion is compounded of two
motions, one circular upon the superficies of a sphere, the other a
straight motion from the centre to every point of the same superficies,
and beyond it.
_A._ I see it.
_B._ It follows hence, that the sun by this motion must every way repel
the air; and since there is no empty place for retiring, the air must
turn about in a circular stream; but slower or swifter according as it
is more or less remote from the sun; and that according to the nature of
fluids, the particles of the air must continually change place with one
another; and also that the stream of the air shall be the contrary way
to that of the motion, for else the air cannot be repelled.
_A._ All this is certain.
_B._ Well; then if you suppose the globe of the earth to be in this
stream which is made by the motion of the sun’s body from east to west,
the stream of air wherein is the earth’s annual motion will be from west
to east.
_A._ It is certain.
_B._ Well. Then if you suppose the globe of the earth, whose circle is
moved annually, to be _l m_, the stream of the air without the ecliptic
falling upon the superficies of the earth _l m_ without the ecliptic,
being slower, and the stream that falleth within swifter, the earth
shall be turned upon its own centre proportionally to the greatness of
the circles; and consequently their diameters shall be parallel; as also
are other straight lines correspondent.
_A._ I deny not but the streams are as you say; and confess that the
proportion of the swiftness without, is to the swiftness within, as the
sun’s ecliptic to the ecliptic of the earth; that is to say, as the
angle H A B to the angle _m_ B _b_. And I like your argument the better,
because it is drawn from Copernicus his foundation. I mean the
compounded motion of straight and circular.
_B._ I think I shall not offer you many demonstrations of physical
conclusions that are not derived from the motions supposed or proved by
Copernicus. For those conclusions in natural philosophy I most suspect
of falshood, which require most variety of suppositions for their
demonstrations.
_A._ The next thing I would know, is how great or little you suppose
that circle _a_ M?
_B._ I suppose it less than you can make it: for there appears in the
sun no such motion sensible. It is the first endeavour of the sun’s
motion. But for all that, as small as the circle is, the motion may be
as swift, and of as great strength as it is possible to be named. It is
but a kind of trembling that necessarily happeneth in those bodies,
which with great resistance press upon one another.
_A._ I understand now from what cause proceedeth the annual motion. Is
the sun the cause also of the diurnal motion?
_B._ Not the immediate cause. For the diurnal motion of the earth is
upon its own centre, and therefore the sun’s motion cannot describe it.
But it proceedeth as a necessary consequence from the annual motion. For
which I have both experience and demonstration. The experiment is this:
into a large hemisphere of wood, spherically concave, put in a globe of
lead, and with your hands hold it fast by the brim, moving your hand
circularly, but in a very small compass; you shall see the globe
circulate about the concave vessel, just in the same manner as the earth
doth every year in the air; and you shall see withal, that as it goes,
it turns perpetually upon its own centre, and very swiftly.
_A._ I have seen it: and it is used in some great kitchens to grind
mustard.
_B._ Is it so? Therefore take a hemisphere of gold, if you have it, the
greater the better, and a bullet of gold, and, without mustard, you
shall see the same effect.
_A._ I doubt it not. But the cause of it is evident. For any spherical
body being in motion upon the sides of a concave and hard sphere, is all
the way turned upon its own centre by the resistance of the hard wood or
metal. But the earth is a bullet without weight, and meeteth only with
air, without any harder body in the way to resist it.
_B._ Do you think the air makes no resistance, especially to so swift a
motion as is the annual motion of the earth? If it do make any
resistance, you cannot doubt but that it shall turn the earth
circularly, and in a contrary way to its annual motion; that is to say,
from east to west, because the annual motion is from west to east.
_A._ I confess it. But what deduce you from these motions of the sun?
_B._ I deduce, first, that the air must of necessity be moved both
circularly about the body of the sun according to the ecliptic, and also
every way directly from it. For the motion of the sun’s body is
compounded of this circular motion upon the sphere L M, and of the
straight motion of its semi-diameters from the centre A to the
superficies of the sun’s body, which is L M. And therefore the air must
needs be repelled every way, and also continually change place to fill
up the places forsaken by other parts of the air, which else would be
empty, there being no vacuum to retire unto. So that there would be a
perpetual stream of air, and in a contrary way to the motion of the
sun’s body, such as is the motion of water by the sides of a ship under
sail.
_A._ But this motion of the earth from west to east is only circular,
such as is described by a compass about a centre; and cannot therefore
repel the air as the sun does. And the disciples of Copernicus will have
it to be the cause of the moon’s monthly motion about the earth.
_B._ And I think Copernicus himself would have said the same, if his
purpose had been to have shown the natural causes of the motions of the
stars. But that was no part of his design; which was only from his own
observations, and those of former astronomers, to compute the times of
their motions; partly to foretel the conjunctions, oppositions, and
other aspects of the planets; and partly to regulate the times of the
Church’s festivals. But his followers, Kepler and Galileo, make the
earth’s motion to be the efficient cause of the monthly motion of the
moon about the earth; which without the like motion to that of the sun
in L M, is impossible. Let us therefore for the present take it in as a
necessary hypothesis; which from some experiment that I shall produce in
our following discourses, may prove to be a certain truth.
_A._ But seeing A is the centre both of the sun’s body and of the annual
motion of the earth, how can it be (as all astronomers say it is) that
the orb of the annual motion of the earth should be eccentric to the
sun’s body? For you know that from the vernal equinox to the autumnal,
there be one hundred and eighty-seven days; but from the autumnal
equinox to the vernal, there be but one hundred and seventy-eight days.
What natural cause can you assign for this eccentricity?
_B._ Kepler ascribes it to a magnetic virtue, viz. that one part of the
earth’s superficies has a greater kindness for the sun than the other
part.
_A._ I am not satisfied with that. It is magical rather than natural,
and unworthy of Kepler. Tell me your own opinion of it.
_B._ I think that the magnetical virtue he speaks of, consisteth in
this: that the southern hemisphere of the earth is for the greatest part
sea, and that the greatest part of the northern hemisphere is dry land.
But how it is possible that from thence should proceed the eccentricity
(the sun being nearest to the earth, when he is in the winter solstice),
I shall show you when we come to speak of the motions of air and water.
_A._ That is time enough: for I intend it for our next meeting. In the
mean time I pray you tell me what you think to be the cause why the
equinoctial, and consequently the solstitial, points are not always in
one and the same point of the ecliptic of the fixed stars. I know they
are not, because the sun does not rise and set in points diametrically
opposite: for if it did, there would be no difference of the seasons of
the year.
_B._ The cause of that can be no other, than that the earth, which is _l
m_, hath the like motion to that which I suppose the sun to have in L M,
compounded of straight and circular from west to east in a day, as the
annual motion hath in a year; so that, not reckoning the eccentricity,
it will be moved through the ecliptics in one revolution, as Copernicus
proveth, about one degree. Suppose then the whole earth moved from H to
I, (which is half the year) circularly, but falling from I to _i_ in the
same time about thirty minutes, and as much in the other hemisphere from
H to _k_; then draw the line _i k_, which will be equal and parallel to
H I, and be the diameter of the equator for the next year. But it shall
not cut the diameter of the ecliptic B Z in A, which was the equinoctial
of the former year, but in _o_ thirty-six seconds from the first degree
of Aries. Suppose the same done in the hemisphere under the plane of the
paper, and so you have the double of thirty-six seconds, that is
seventy-two seconds, or very near, for the progress of the vernal
equinox in a year. The cause why I suppose the arch I _i_ to be half a
degree in the ecliptic of the earth, is, that Copernicus and other
astronomers, and experience, agree in this, that the equinoctial points
proceed according to the order of the signs, Aries, Taurus, Gemini, &c.
from west to east every hundredth year one degree or very near.
_A._ In what time do they make the whole revolution through the ecliptic
of the sky?
_B._ That you may reckon. For we know by experience that it hath
proceeded about one degree, that is sixty minutes, constantly a long
time in a hundred years. But as one hundred years to one degree, so is
thirty-six thousand years to three hundred and sixty degrees. Also as
one hundred years to one degree, so is one year to the hundredth part of
one degree, or sixty minutes; which is (60)/(100), or thirty-six seconds
for the progress of one year; which must be somewhat more than a degree
according to Copernicus, who, (lib. iii. cap. 2) saith, that for four
hundred years before Ptolomy it was one degree almost constantly. Which
is well enough as to the natural cause of the precession of the
equinoctial points, which is the often-said compounded motion, though
not an exact astronomical calculation.
_A._ And it is a great sign that his supposition is true. But what is
the cause that the obliquity of the ecliptic, that is, the distance
between the equinoctial and the solstice, is not always the same?
_B._ The necessity of the obliquity of the ecliptic is but a consequence
to the precession of the equinoctial points. And therefore, if from C,
the north pole, you make a little circle, C _u_, equal to fifteen
minutes of a degree upon the earth, and another, _u s_, equal to the
same, which will appear like this figure 8, that is, (as Copernicus
calls it), a circle twined, the pole C will be moved half the time of
the equinoctial points, in the arc C _u_, and as much in the alternate
arc _u s_ descending to _s_. But in the arc _s u_, and its alternate
rising to C, the cause of the twining is the earth’s annual motion the
same way in the ecliptic, and makes the four quarters of it; and makes
also their revolution twice as slow as that of the equinoctial points.
And, therefore, the motion of it is the same compounded motion which
Copernicus takes for his supposition, and is the cause of the precession
of the equinoctial points, and consequently of the variation of the
obliquity, adding to it or taking from it somewhere more, somewhere
less; so as that one with another the addition is not much more, nor the
subtraction much less than thirty minutes. But as for the natural
efficient cause of this compounded motion, either in the sun, or the
earth, or any other natural body, it can be none but the immediate hand
of the Creator.
_A._ By this it seems that the poles of the earth are always the same,
but make this 8 in the sphere of the fixed stars near that which is
called Cynosura.
_B._ No: it is described on the earth, but the annual motion describes a
circle in the sphere of the fixed stars. Though I think it improper to
say a sphere of the fixed stars, when it is so unlikely that all the
fixed stars should be in the superficies of one and the same globe.
_A._ I do not believe they are.
_B._ Nor I, since they may seem less one than another, as well by their
different distances, as by their different magnitudes. Nor is it likely
that the sun (which is a fixed star) is the efficient cause of the
motion of those remoter planets, Mars, Jupiter, and Saturn; seeing the
whole sphere, whose diameter is the distance between the sun and the
earth, is but a point in respect of the distance between the sun and any
other fixed star. Which I say only to excite those that value the
knowledge of the cause of comets, to look for it in the dominion of some
other sun than that which moveth the earth. For why may not there be
some other fixed star, nearer to some planet than is the sun, and cause
such a light in it as we call a comet?
_A._ As how?
_B._ You have seen how in high and thin clouds above the earth, the
sun-beams piercing them have appeared like a beard; and why might not
such a beard have appeared to you like a comet, if you had looked upon
it from as high as some of the fixed stars?
_A._ But because it is a thing impossible for me to know, I will proceed
in my own way of inquiry. And seeing you ascribe this compounded motion
to the sun and earth, I would grant you that the earth (whose annual
motion is from west to east) shall give the moon her monthly motion from
east to west. But then I ask you whether the moon have also that
compounded motion of the earth, and with it a motion upon its own
centre, as hath the earth? For seeing the moon has no other planet to
carry about her, she needs it not.
_B._ I see reason enough, and some necessity, that the moon should have
both those motions. For you cannot think that the Creator of the stars,
when he gave them their circular motion, did first take a centre, and
then describe a circle with a chain or compass, as men do? No; he moved
all the parts of a star together and equally in the creation: and that
is the reason I give you. The necessity of it comes from this
phenomenon, that the moon doth turn one and the same face towards the
earth; which cannot be by being moved about the earth parallelly, unless
also it turn about its own centre. Besides, we know by experience, that
the motion of the moon doth add not a little to the motion of the sea:
which were impossible if it did not add to the stream of the air, and by
consequence to that of the water.
_A._ If you could get a piece of the true and intimate substance of the
earth, of the bigness of a musket-bullet, do you believe that the bullet
would have the like compounded motion to that which you attribute to the
sun, earth, and moon?
_B._ Yes, truly; but with less strength, according to its magnitude;
saving that by its gravity falling to the earth, the activity of it
would be unperceived.
_A._ I will trouble you no more with the nature of celestial
appearances; but I pray you tell me by what art a man may find what part
of a circle the diameter of the sun’s body doth subtend in the ecliptic
circle?
_B._ Kepler says it subtends thirty minutes, which is half a degree. His
way to find it is by letting in the sun-beams into a close room through
a small hole, and receiving the image of it upon a plane
perpendicularly. For by this means he hath a triangle, whose sides and
angles he can know by measure; and the vertical angle he seeks for, and
the substance of the arc of the sun’s body.
_A._ But I think it impossible to distinguish where the part illuminate
toucheth the part not illuminate.
_B._ Another way is this: upon the equinoctial day, with a watch that
shows the minutes standing by you, observe when the lower brim of the
sun’s setting first comes to the horizon, and set the index to some
minute of the watch; and observe again the upper brim when it comes to
the horizon: then count the minutes, and you have what you look for.
Other way I know none.
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