William Whewell.

Astronomy and general physics considered with reference to natural theology online

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it appeared that this line ought to move round once in
eighteen years; according to observation, it moves
round once in nine years. This difference, the only


obvious failure of the theory of gravitation, embarrassed
mathematicians exceedingly. It is true, it was subse-
quently discovered that the apparent discrepancy arose
from a mistake; the calculation, which is long and
laborious, was supposed to have been carried far enough
to get close to the truth ; but it appeared afterwards
that the residue which had been left out as insignificant,
produced, by an unexpected turn in the reckoning, an
effect as large as that which had been taken for the
whole. But this discovery was not made till a later
period ; and in the mean time the law of the inverse
square appeared to be at fault. Clairault tried to
remedy the defect by supposing that the force of the
earth's gravity consisted of a large force varying in-
versely as the square of the distance, and a very small
force varying inversely as the fourth power (the square
of the square). By such a supposition, observation and
theory could be reconciled ; but on the suggestion of it,
Buffon came forward with the assertion that the force
could not vary according to any other law than the in-
verse square. His arguments are rather metaphysical
than physical or mathematical. Gravity, he urges^ is a
quality, an emanation ; and all emanations are inversely
as the square of the distance, as light, odours. To this
Clairault repHes by asking how we know .that light and
odours have their intensity inversel}^ as the square of
the distance from their origin : not, he observes, by mea-
suring the intensity, but by supposing these effects to be
material emanations. But who, he asks, supposes gTa-
vity to be a material emanation fivm the attracting body.
Buffon again pleads that so many facts prove the

o 2


law of the inverse square, that a single one, which
occurs to interfere with this agreement, must be in
some manner capable of being explained away.
Clairault replies, that the facts do not i^rove this law
to obtain exactly ; that small effects, of the same order
as the one under discussion, have been neglected in
the supposed proof; and that therefore the law is only
known to be true, as far as such an approximation goes,
and no farther.

Buffon then argues, that there can be no such addi-
tional fraction of the force, following a different law, as
Clairault supposes : for what, he asks, is there to
determine the magnitude of the fraction to one amount
rather than another ? why should nature select for it
any particular magnitude ? To this it is replied, that,
whether we can explain the fact or not, nature does
select certain magnitudes in preference to others ; that
where we ascertain she does this, we are not to deny
the fact because we cannot assign the grounds of her
preference. What is there, it is asked, to determine
the magnitude of the whole force at any fixed distance?
We cannot tell ; yet the force is of a certain definite
intensity and no other.

Finally Clairault observes, that we have, in cohesion,
capillary attraction, and various other cases, examples
of forces varying according to other laws than the in-
verse square ; and that therefore this cannot be the
only possible law.

The discrepancy between observation and theory
which gave rise to this controversy was removed, as has
been alrea<ly stated, by a more exact calculation : and


thus, as Laplace observes, in this case the metaphy-
sician turned out to be right and the mathematician to
be v^rong. But most persons, probably, who are
familiar with such trains of speculation, will allow, that
Clairault had the best of the argument, and that the
attempts to show the law of gravitation to be neces-
sarily what it is, are fallacious and unsound.

VIII. We may observe, however, that the law of
gravitation according to the inverse square of the dis-
tance, which thus regulates the motions of the solar
system, is not confined to that province of the universe,
as has been shown by recent researches. It appears
by the observations and calculations of Sir John
Herschel, that several of the stars, called double stars,
consist of a pair of luminous bodies which revolve
about each other in ellipses, in such a manner as to
show^ that the force, by which they are attracted to
each other, varies according to the law of the inverse
square. We thus learn a remarkable fact concerning
bodies which seemed so far removed from us that no
effort of our science could reach them; and we find
that the same law of mutual attraction which we have
before traced to the farthest bounds of the solar system,
prevails also in spaces at a distance compared with
which the orbit of Saturn shrinks into a point. The
establishment of such a truth certainly suggests, as
highly probable, the jprevalence of this law among all
the bodies of the universe. And we may therefore
suppose, that the same ordinance which gave to the
parts of our system that rule by which they fulfil the
purposes of their creation, impressed the same rule on


the other portions of matter which are scattered in the
most remote parts of the universe ; and thus gave to
their movements the same grounds of simplicity and
harmony which we find reason to admire, as far as we
can acquire any knowledge of our own more immediate

Chap. XI. — The Laws of Motion,

We shall now make a few remarks on the general
Laws of Motion by which all mechanical effects take
place. Are we to consider these as instituted laws?
And if so, can we point out any of the reasons which
we may suppose to have led to the selection of those
laws which really exist ?

The observations formerly made concerning the
inevitable narrowness and imperfection of our conclu-
sions on such subjects, apply here, even more strongly
than in the case of the law of gravitation. We can
hardly conceive matter divested of these laws ; and we
cannot perceive or trace a millionth part of the effects
which they produce. We cannot, therefore, expect to
go far in pointing out the essential advantages of these
laws such as they now obtain.

It would be easy to show that the fundamental laws
of motion, in whatever form we state them, possess a
very pre-eminent simplicity, compared with almost all
others, which we might imagine as existing. This
simplicity has indeed produced an effect on men's minds
which, though delusive, appears to be very natural;
several writers have treated these laws as self-evident, and


necessarily flowing from the nature of our conceptions.
We conceive that this is an erroneous view, and that
these laws are known to us to be what they are, by
experience only; that the laws of motion might,
so far as we can discern, have been any others, j
They appear therefore to be selected for their fitness
to answer their purposes; and we may, perhaps, be
able to point out some instances in which this fitness is
apparent to us,

Newton, and many English philosophers, teach the
existence of three separate fundamental laws of motion,
while most of the eminent mathematicians of France
reduce these to two, the law of inertia and the law that
force is ]3i^oportional to velocity. As an example of
the views which we wish to illustrate, we may take the
law of inertia, which is identical with Newton's first
Law of Motion. This law asserts, that a body at
rest continues at rest, and that a body in motion goes
on moving with its velocity and direction unchanged,
except so far as it is acted on by extraneous forces*

We conceive that this law, simple and universal as
it is, cannot be shown to be necessarily true. It might
be difficult to discuss this point in general terms with
any clearness ; but let us take the only example which

^ If the laws of motion are stated as three, wjiich we conceive to be
tliQ true view of the subject, the other two, as applied in mechanical
reasonings, are the following : —

Second Law. When a force acts on a body in motion, it produces the
same effect as if the same force acted on a body at rest-

Third Law. When a force of the nature of pressure produces motion,
the velocity produced is proportional to the force, other things being


we know of a motion absolutely uniform, in conse-
quence of the absence of any force to accelerate or
retard it ; — this motion is the rotation of the earth on
its axis.

I. It is scarcely possible that discussions on such
subjects should not have a repulsive and scholastic
aspect, and appear like disputes about words rather than
things. For mechanical writers have exercised all
their ingenuity so to circumscribe their notions and so
to define their terms, that these fundamental truths
should be expressed in the simplest manner : the con-
sequence of which has been, that they have been made
to assume the appearance rather of identical assertions
than of general facts of exj)erience. But in order to
avoid this inconvenience, as far as may be, we take the
first law of motion as exemplified in a particular case,
the rotation of the earth. Of all the motions with
which we are acquainted, this alone is invariable. Each
day, measm-ed b}^ the passages of the stars, is so pre-
cisely of the same length, that, according to Laplace's
calculations, it is impossible that a difference of one
hundredth of a second of time should have obtained
between the length of the day in the earliest ages and
at the present time. Now why is this ? How is this
ver^^ remarkable uniformity preserved in this particular
phenomenon, while all the other motions of the system
are subject to inequalities ? How is it that in the celestial
machine no retardation takes place by the lapse of
time, as would be the case in any machine which it
would be possible for human powers to construct?
The answer is, that in tjie earth's revolution on her


axis no cause operates to retard the speed, like the
imperfection of materials, the friction of supports, the
resistance of the ambient medium ; * impediments
which cannot, in any human mechanism, however perfect,
be completely annihilated. But here we are led to ask
again, why should the speed continue the same when
not affected by an extraneous cause ? why should it not
languish and deca}^ of itself by the mere lapse of time ?
That it might do so, involves no contradiction, for it
was the common, though erroneous, belief of all mecha-
nical speculators, to the time of Galileo. We can
conceive velocity to diminish in proceeding from a
certain point of time, as easily as we can conceive force
to diminish in proceeding from a certain point of space,
which in attractive forces really occurs. But, it is
sometimes said, the motion (that is the velocity) must
continue the same from one instant to another, for
there is nothing to change it. This appears to be
taking refuge in words. We may call the velocity, that
is the speed of a body, its motion ; but we cannot, by
giving it this name, make it a thing which has any
a priori claim to permanence, much less any self-
evident constancy. Why must the speed of a body,
left to itself, continue the same, any more than its

* It has already been stated that the resisting medium spoken of in
Chapter VIII. of this Book has not yet produced any effect which can
be detected in the motion of the earth. Probably the effect of this
medium upon the rotation of the earth would be extremely small com-
pared with its effect on the earth's motion in her orbit ; and yet this
latter effect bears no discoverable proportion to the effect of the smallest
perturbing forces of the other planets.


temperature. Hot bodies grow cooler when left to
themselves; why should not quick bodies go slower when
left to themselves ? Why must a body describe 1000
feet in the next second because it has described 1000
feet in the last? Nothing but experience, under
proper circumstances, can inform us whether bodies,
abstracting from external agency, do move according
to such a rule. We find that they do so: we learn
that all diminution of their speed which ever takes
place, can be traced to external causes. Contrary to
all that men had guessed, motion appears to be of
itself endless and unwearied. In order to account for
the unalterable permanence of the length of our day,
all that is requisite is to show that there is no let or
hindrance in the way of the earth's rotation; — no
resisting medium or alteration of size — she " spinning
sleeps " on her axle, as the poet expresses it, and may
go on sleeping with the same regularity for ever, so
far as the experimental properties of motion are con-

Such is the necessary consequence of the first law of
motion ; but the law itself has no necessary existence,
so far as we can see. It was discovered only after
various perplexities and false conjectures of speculators
on mechanics. We have learnt that it is so, but we
have not learnt, nor can any one undertake to teach us,
that it must have been so. For aught we can tell, it is
one among a thousand equally possible laws, which
might have regulated the motions of bodies.

II. But though we have thus no reason to consider
this as the only possible law, we have good reason to


consider it as the best, or at least as iDOSsessing all that
we can conceive of advantage. It is the simplest con-
ceivable of such laws. If the velocity had been com-
pelled to change with the time, there must have been a
law of the change, and the kind and amount of this
change must have been determined by its dependence
on the time and other conditions. This, though quite
supposable, would undoubtedly have been more complex
than the present state of things. And though com-
plexity does not appear to embarrass the operation of
the laws of nature, and is admitted, without scruple,
when there is reason for it, simplicity is the usual
character of such laws, and appears to have been a
ground of selection in the formation of the universe,
as it is a mark of beauty to us in our contemplation
of it.

But there is a still stronger apparent reason for the
selection of this law of the preservation of motion. If
the case had been otherwise, the universe must neces-
sarily in the course of ages have been reduced to a
state of rest, or at least to a state not sensibly differing
from it. If the earth's motion, round its axis, had
slackened by a very small quantity, for instance, by a
hundredth of a second in a revolution, and in this
proportion continued, the day would have been already
lengthened by six hours in the 6000 years which have
elapsed since the history of the world began ; and if we
suppose a longer period to precede or to follow, the day
might be increased to a month or to any length. All
the adaptations which depend on the length of the day,
would consequently be deranged. But this would not


be all ; for the same law of motion is equally requisite
for the preservation of the anr.ual motion of the earth.
If her motion were retarded by the establishment of
any other law instead of the existing one, she would
wheel nearer and nearer to the sun at every revolution,
and at last reach the centre, like a falling lioox^. The
same would happen to the other planets ; and the whole
solar system would, in the course of a certain period,
be gathered into a heap of matter without life or
motion. In the present state of things on the other
hand, the system, as we have already explained, is, b}'-
a combination of remarkable provisions, calculated for
an almost indefinite existence, of undiminished fitness
for its purposes.

There are, therefore, manifest reasons, why, of all
laws which could occupy the place of the first law of
motion, the one which now obtains is the only one
consistent with the durability and uniformity of the
system ; — the one, therefore, which we may naturally
conceive to be selected by a wise contriver. And as,
along with this, it has appeared that we have no sort of
right to attribute the establishment of this law to any-
thing but selection, we have here a striking evidence of
design, suited to lead us to a perception of that Divine
mind, by which means so simple are made to answer
purposes so extensive and so beneficial.


Chap. XII. — Friction*

We shall not pursue this argument of the last chapter,
hy considering the other laws of motion in the same
manner as we have there considered the first, which
might be done. But the facts which form exceptions
and apparent contradictions to the first law of which
we have been treating, and which are very numerous,
offer, we conceive, an additional exemplification of
the same argument; and this we shall endeavour to

The rule that a body naturally moves for ever with
an undiminished speed, is so far from being obviously
true, that it appears on a first examination to be mani-
festly false. The hoop of the school-boy, left to itself,
runs on a short distance, and then stops ; his top spins
a little while, but finally, flags and falls ; all motion on
the earth appears to decay by its own nature; all
matter which we move appears to have a perpetual
tendency to divest itself of the velocity which we com-
municate to it. How is this reconcilable with the first
law of motion on which we have been insisting ?

It is reconciled principally by considering the effect
of Friction. Among terrestrial objects friction exerts
an agency almost as universal and constant as the laws

* Though Friction is not obviously concerned in any cosmical
phenomena, we have thought this the proper place to introduce the
consideration of it ; since the contrast between the cases in which it
does act, and those in which it does not, is best illustrated by a com-
parison of cosmical with terrestrial motions.


of motion themselves ; an agency which completely
changes and disguises the results of those laws. AVe
shall consider soilie of these effects.

It is probably not necessary to explain at any length
the nature and operation of friction. When a body
cannot move without causing two surfaces to rub toge-
ther, this rubbing has a tendency to diminish the body's
motion or to prevent it entirely. If the body of a car-
riage be placed on the earth without the wheels, a
considerable force will be requisite in order to move
it at all: it is here the friction against the ground
which obstructs the motion. If the carriage be placed
on its wheels, a much less force will move it, but if
moved it will soon stop : it is the friction at the ground
and at the axles which stops it : placed on a level rail-
road, with well made and well oiled wheels, and once
put in motion, it might run a considerable distance
alone, for the friction is here much less ; but there is
friction, and therefore the motion would after a time

The same kind of action between the surfaces of two
bodies which retards and stops theii' motions when
they move touching each other, will also prevent their
moving at all, if the force which urges them into
motion be insufficient to overcome the resistance which
the contact of the suirfaces produces. Friction, as
writers on mechanics use the term, exists not only
when the surfaces rub against each other, but also
when the state of things is such that they would rub if
they did move. It is a force which is called into
action by a tendency to move, and which forbids


motion; it rnay be likened to a chain of a certain
force wliich binds bodies in their places ; and we may
push or pull the bodies without moving them, except
we exert a sufficient force to break this imaginary

I. The friction which we shall princij)ally consider
is the friction which prevents motion. So employed,
friction is one of the most universal and important
agents in the mechanism of our daily comforts and
occupations. It is a force which is called into play
to an extent incomparably greater than aU the other
forces with which we are concerned in the course of our
daily life. We are dexDendent upon it at every instant
and in every action : and it is not possible to enumerate
all the ways in which it serves us ; scarcely even to
suggest a sufficient number of them to give us a true
notion of its functions.

What can appear more simple operations than
standing and walking ? yet it is easy to see that without
the aid of friction these simple actions would scarcely
be possible. Every one knows how difficult and dan-
gerous they are when performed on smooth ice. In such
a situation we cannot always succeed in standing : if the
ice be very smooth, it is by no means easy to walk,
even when the surface is perfectly level ; and if it were
ever so little inclined, no one would make the attempt.
Yet walldng on the ice and on the ground differ only
in our experiencing more friction in the latter case.
We say more, for there is a considerable friction even
in the case of ice, as we see by the small distance which
a stone slides when thrown along the surface. It is


this friction of the earth which, at every step we take,
prevents the foot from sliding hack ; and thus allows
us to push the hody and the other foot forwards. And
when we come to violent bodily motions, to running,
leaping, pulling or pushing objects, it is easily seen how
entirely we depend upon the friction of the ground for
our strength and force. Every one knows how com-
pletely powerless we become in any of these actions by
the foot slipping.

In the same manner it is the friction of objects to
which the hand is applied, which enables us to hold
them with any degree of firmness. In some contests
it was formerly the custom for the combatants to rub
their bodies with oil, that the adversary might not be
able to keep his grasp. If the pole of the boatman,
the rope of the sailor, were thus smooth and lubricated,
how weak would be the thrust and the pull ! Yet this
would only be the removal of friction.

Our buildings are no less dependent on this force
for their stability. Some edifices are erected without
the aid of cement : and if the stones be large and well
squared, such structures may be highly substantial and
durable ; even when rude and slight, houses so built
answer the purposes of life. These are entirely upheld
by friction, and without the support of that agent they
would be thrown down by the ze^^hyr, far more easily
than if all the stones were lumps of ice with a thawing
surface. But even in cases where cement hinds the
masonry, it does not take the duty of holding it toge-
ther. In consequence of the existence of friction, there
is no constant tendency of the stones to separate ; thisy


are in a state of repose. If this were not so, if every
shock and every breeze required to be counteracted by
the cement, no composition exists which would long
sustain such a wear and tear. The cement excludes
the corroding elements, and helps to resist extraordi-
nary violence ; but it is friction which gives the habitual
state of rest.

We are not to consider friction as a small force,
slightly modifying the effects of other agencies. On
the contrary its amount is in most cases very great.
When a body lies loose on the ground, the friction is
equal to one third or one half, or in some cases the
whole, of its weight. But in cases of bodies supported
by oblique pressure, the amount is far more enormous.
In the arch of a bridge, the friction which is called
into play between two of the vaulting stones, may be
equal to the whole weight of the bridge. In such
cases this conservative force is so great, that the
common theory, which neglects it, does not help us
even to guess what will take place. According to the
theory, certain forms of arches only will stand; but
in practice almost any form will stand, and it is not
easy to construct a model of a bridge which will fall.

We may see the great force of friction in the brake,
by which a large weight running down a long inclined
plane has its motion moderated and stopped ; in the
windlass, where a few coils of the rope round a cylinder
sustain the stress and weight of a large iron anchor ;
in the nail or screw which holds together large beams ;
in the mode of raising large blocks of granite by an
iron rod driven into a hole in the stone. Probably

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Online LibraryWilliam WhewellAstronomy and general physics considered with reference to natural theology → online text (page 14 of 22)