Newton's Principia: Definitions: Scholium
From: Isaac Newton (eric_baird_at_compuserve.com)
Date: 11/14/04
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Date: Sun, 14 Nov 2004 03:43:58 +0000 (UTC)
[ quote starts ]
: SCHOLIUM
Hitherto I have laid down the definitions of such words as are less
known, and explained the sense in which I would have them to be
understood in the following discourse. I do not define time, space,
place, and motion, as being well known to all. Only I must observe,
that the common people conceive those quantities under no other
notions but from the relation they bear to sensible objects. And
thence arise certain prejudices, for the removing of which it will be
convenient to distinguish them into absolute and relative, true and
apparent, mathematical and common.
I. Absolute, true, and mathematical time, of itself, and from its
own nature, flows equably without relation to anything external, and
by another name is called duration: relative, apparent, and common
time, is some sensible and external (whether accurate or unequable)
measure of duration by the means of motion, which is commonly used
instead of true time; such as an hour, a day, a month, a year.
II. Absolute space, in its own nature, without relation to
anything external, remains always similar and immovable. Relative
space is some movable dimension or measure of the absolute spaces;
which our senses determine by its position to bodies; and which is
commonly taken for immovable space; such is the dimension of a
subterraneous, an aerial, or celestial space, determined by its
position in respect of the earth. Absolute and relative space are the
same in figure and magnitude; but they do not remain always
numerically the same. For if the earth, for instance, moves, a space
of our air, which relatively and in respect of the earth remains
always the same, will at one time be one part of the absolute space
into which the air passes; at another time it will be another part of
the same, and so, absolutely understood, it will be continually
changed.
III. Place is a part of space which a body takes up, and is
according to the space, either absolute or relative. I say, a part of
space; not the situation, nor the external surface of the body. For
the places of equal solids are always equal; but their surfaces, by
reason of their dissimilar figures, are often unequal. Positions
properly have no quantity, nor are they so much the places themselves,
as the properties of places. The motion of the whole is the same with
the sum of the motions of the parts; that is, the translation of the
whole, out of its place, is the same thing with the sum of the
translations of the parts out of their places; and therefore the place
of the whole is the same as the sum of the places of the parts, and
for that reason, it is internal, and in the whole body.
IV. Absolute motion is the translation of a body from one absolute
place into another; and relative motion, the translation from one
relative place into another. Thus in a ship under sail, the relative
place of a body is that part of the ship which the body possesses; or
that part of the cavity which the body fills, and which therefore
moves together with the ship: and relative rest is the continuance of
the body in the same part of the ship, or of its cavity. But real,
absolute rest, is the continuance of the body in the same part of that
immovable space, in which the ship itself, its cavity, and all that it
contains, is moved. Wherefore, if the earth is really at rest, the
body, which relatively rests in the ship, will really and absolutely
move with the same velocity which the ship has on the earth. But if
the earth also moves, the true and absolute motion of the body will
arise, partly from the true motion of the earth, in immovable space,
partly from the relative motion of the ship on the earth; and if the
body moves also relatively in the ship, its true motion will arise,
partly from the true motion of the earth, in immovable space, and
partly from the relative motions as well of the ship on the earth, as
of the body in the ship; and from these relative motions will arise
the relative motion of the body on the earth. As if that part of the
earth, where the ship is, was truly moved towards the cast, with a
velocity of 10010 parts; while the ship itself, with a fresh gale, and
full sails, is carried towards the west, with a velocity expressed by
10 of those parts; but a sailor walks in the ship towards the cast,
with 1 part of the said velocity; then the sailor will be moved truly
in immovable space towards the east, with a velocity of 10001 parts,
and relatively on the earth towards the west, with a velocity of 9 of
those parts.
Absolute time, in astronomy, is distinguished from relative, by the
equation or correction of the apparent time. For the natural days are
truly unequal, though they are commonly considered as equal, and used
for a measure of time; astronomers correct this inequality that they
may measure the celestial motions by a more accurate time. It may be,
that there is no such thing as an equable motion, whereby time may be
accurately measured. All motions may he accelerated and retarded, but
the flowing of absolute time is not liable to any change. The duration
or perseverance of the existence of things remains the same, whether
the motions are swift or slow, or none at all: and therefore this
duration ought to be distinguished from what are only sensible
measures thereof; and from which we deduce it, by means of the
astronomical equation. The necessity of this equation, for determining
the times of a phenomenon, is evinced as well from the experiments of
the pendulum clock, as by eclipses of the satellites of Jupiter.
As the order of the parts of time is immutable, so also is the order
of the parts of space. Suppose those parts to be moved out of their
places, and they will be moved (if the expression may he allowed) out
of themselves. For times and spaces are, as it were, the places as
well of themselves as of all other things. All things are placed in
time as to order of succession; and in space as to order of situation.
It is from their essence or nature that they are places; and that the
primary places of things should be movable, is absurd. These are
therefore the absolute places; and translations out of those places,
are the only absolute motions.
But because the parts of space cannot be seen, or distinguished from
one another by our senses, therefore in their stead we use sensible
measures of them. For from the positions and distances of things from
any body considered as immovable, we define all places; and then with
respect to such places, we estimate all motions, considering bodies as
transferred from some of those places into others. And so, instead of
absolute places and motions, we use relative ones; and that without
any inconvenience in common affairs; but in philosophical
disquisitions, we ought to abstract from our senses, and consider
things themselves, distinct from what are only sensible measures of
them. For it may be that there is no body really at rest, to which the
places and motions of others may be referred.
But we may distinguish rest and motion, absolute and relative, one
from the other by their properties, causes, and effects. It is a
property of rest, that bodies really at rest do rest in respect to one
another. And therefore as it is possible, that in the remote regions
of the fixed stars, or perhaps far beyond them, there may be some body
absolutely at rest; but impossible to know, from the position of
bodies to one another in our regions, whether any of these do keep the
same position to that remote body, it follows that absolute rest
cannot be determined from the position of bodies in our regions.
It is a property of motion, that the parts, which retain given
positions to their wholes, do partake of the motions of those wholes.
For all the parts of revolving bodies endeavor to recede from the axis
of motion; and the impetus of bodies moving forwards arises from the
joint impetus of all the parts. Therefore, if surrounding bodies are
moved, those that are relatively at rest within them will partake of
their motion. Upon which account, the true and absolute motion of a
body cannot be determined by the translation of it from those which
only seem to rest; for the external bodies ought not only to appear at
rest, but to be really at rest. For otherwise, all included bodies,
besides their translation from near the surrounding ones, partake
likewise of their true motions; and though that translation were not
made, they would not be really at rest, but only seem to be so. For
the surrounding bodies stand in the like relation to the surrounded as
the exterior part of a whole does to the interior, or as the shell
does to the kernel; but if the shell moves, the kernel will also move,
as being part of the whole, without any removal from near the shell.
A property, near akin to the preceding, is this, that if a place is
moved, whatever is placed therein moves along with it; and therefore a
body, which is moved from a place in motion, partakes also of the
motion of its place. Upon which account, all motions, from places in
motion, are no other than parts of entire and absolute motions; and
every entire motion is composed of the motion of the body out of its
first place, and the motion of this place out of its place; and so on,
until we come to some immovable place, as in the before?mentioned
example of the sailor. Wherefore, entire and absolute motions can be
no otherwise determined than by immovable places; and for that reason
I did before refer those absolute motions to immovable places, but
relative ones to movable places. Now no other places are immovable but
those that, from infinity to infinity, do all retain the same given
position one to another; and upon this account must ever remain
unmoved; and do thereby constitute immovable space.
The causes by which true and relative motions are distinguished, one
from the other, are the forces impressed upon bodies to generate
motion. True motion is neither generated nor altered, but by some
force impressed upon the body moved; but relative motion may be
generated or altered without any force impressed upon the body. For it
is sufficient only to impress some force on other bodies with which
the former is compared, that by their giving way, that relation may be
changed, in which the relative rest or motion of this other body did
consist. Again, true motion suffers always some change from any force
impressed upon the moving body; but relative motion does not
necessarily undergo any change by such forces. For if the same forces
are likewise impressed on those other bodies, with which the
comparison is made, that the relative position may be preserved, then
that condition will be preserved in which the relative motion
consists. And therefore any relative motion may be changed when the
true motion remains unaltered, and the relative may be preserved when
the true suffers some change. Thus, true motion by no means consists
in such relations.
The effects which distinguish absolute from relative motion are, the
forces of receding from the axis of circular motion. For there are no
such forces in a circular motion purely relative, but in a true and
absolute circular motion, they are greater or less, according to the
quantity of the motion. If a vessel, hung by a long cord, is so often
turned about that the cord is strongly twisted, then filled with
water, and held at rest together with the water; thereupon, by the
sudden action of another force, it is whirled about the contrary way,
and while the cord is untwisting itself, the vessel continues for some
time in this motion; the surface of the water will at first be plain,
as before the vessel began to move; but after that, the vessel, by
gradually communicating its motion to the water, will make it begin
sensibly to revolve, and recede by little and little from the middle,
and ascend to the sides of the vessel, forming itself into a concave
figure (as I have experienced ), and the swifter the motion becomes,
the higher will the water rise, till at last, performing its
revolutions in the same times with the vessel, it becomes relatively
at rest in it. This ascent of the water shows its endeavor to recede
from the axis of its motion; and the true and absolute circular motion
of the water, which is here directly contrary to the relative, becomes
known, and may be measured by this endeavor. At first, when the
relative motion of the water in the vessel was greatest, it produced
no endeavor to recede from the axis; the water showed no tendency to
the circumference, nor any ascent towards the sides of the vessel, but
remained of a plain surface, and therefore its true circular motion
had not yet begun. But afterwards, when the relative motion of the
water had decreased, the ascent thereof towards the sides of the
vessel proved its endeavor to recede from the axis; and this endeavor
showed the real circular motion of the water continually increasing,
till it had acquired its greatest quantity, when the water rested
relatively in the vessel. And therefore this endeavor does not depend
upon any translation of the water in respect of the ambient bodies,
nor can true circular motion be defined by such translation. There is
only one real circular motion of any one revolving body, corresponding
to only one power of endeavoring to recede from its axis of motion, as
its proper and adequate effect; but relative motions, in one and the
same body, are innumerable, according to the various relations it
bears to external bodies, and, like other relations, are altogether
destitute of any real effect, any otherwise than they may perhaps
partake of that one only true motion. And therefore in their system
who suppose that our heavens, revolving below the sphere of the fixed
stars, carry the planets along with them; the several parts of those
heavens, and the planets, which are indeed relatively at rest in their
heavens, do yet really move. For they change their position one to
another (which never happens to bodies truly at rest), and being
carried together with their heavens, partake of their motions, and as
parts of revolving wholes, endeavor to recede from the axis of their
motions.
Wherefore relative quantities are not the quantities themselves, whose
names they bear, but those sensible measures of them (either accurate
or inaccurate), which are commonly used instead of the measured
quantities themselves. And if the meaning of words is to be determined
by their use, then by the names time, space, place, and motion, their
[sensible] measures are properly to be understood; and the expression
will be unusual, and purely mathematical, if the measured quantities
themselves are meant. On this account, those violate the accuracy of
language, which ought to be kept precise, who interpret these words
for the measured quantities. Nor do those less defile the purity of
mathematical and philosophical truths, who confound real quantities
with their relations and sensible measures.
It is indeed a matter of great difficulty to discover, and effectually
to distinguish, the true motions of particular bodies from the
apparent; because the parts of that immovable space, in which those
motions are performed, do by no means come under the observation of
our senses. Yet the thing is not altogether desperate; for we have
some arguments to guide us, partly from the apparent motions, which
are the differences of the true motions; partly from the forces, which
are the causes and effects of the true motions. For instance, if two
globes, kept at a given distance one from the other by means of a cord
that connects them, were revolved about their common centre of
gravity, we might, from the tension of the cord, discover the endeavor
of the globes to recede from the axis of their motion, and from thence
we might compute the quantity of their circular motions. And then if
any equal forces should be impressed at once on the alternate faces of
the globes to augment or diminish their circular motions, from the
increase or decrease of the tension of the cord, we might infer the
increment or decrement of their motions; and thence would be found on
what faces those forces ought to be impressed, that the motions of the
globes might be most augmented; that is, we might discover their
hindmost faces, or those which, in the circular motion, do follow. But
the faces which follow being known, and consequently the opposite ones
that precede, we should likewise know the determination of their
motions. And thus we might find both the quantity and the
determination of this circular motion, even in an immense vacuum,
where there was nothing external or sensible with which the globes
could be compared. But now, if in that space some remote bodies were
placed that kept always a given position one to another, as the fixed
stars do in our regions, we could not indeed determine from the
relative translation of the globes among those bodies, whether the
motion did belong to the globes or to the bodies. But if we observed
the cord, and found that its tension was that very tension which the
motions of the globes required, we might conclude the motion to be in
the globes, and the bodies to be at rest; and then, lastly, from the
translation of the globes among the bodies, we should find the
determination of their motions. But how we are to obtain the true
motions from their causes, effects, and apparent differences, and the
converse, shall be explained more at large in the following treatise.
For to this end it was that I composed it.
[end of chapter]
( Principia, pp 6 - 12 )
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