_Recapitulation._
1. It has been shown in the preceding chapters that a great number
of quantities and laws appear to have been _selected_ in the
construction of the universe; and that by the adjustment to each
other of the magnitudes and laws thus selected, the constitution
of the world is what we find it, and is fitted for the support
of vegetables and animals, in a manner in which it could not have
been, if the properties and quantities of the elements had been
different from what they are. We shall here recapitulate the
principal of the laws and magnitudes to which this conclusion has
been shown to apply.
1. The Length of the Year, which depends on the force of the
attraction of the sun, and its distance from the earth.
2. The Length of the Day.
3. The Mass of the Earth, which depends on its magnitude and
density.
4. The Magnitude of the Ocean.
5. The Magnitude of the Atmosphere.
6. The Law and Rate of the Conducting Power of the Earth.
7. The Law and Rate of the Radiating Power of the Earth.
8. The Law and Rate of the Expansion of Water by Heat.
9. The Law and Rate of the Expansion of Water by Cold, below 40
degrees.
10. The Law and Quantity of the Expansion of Water in Freezing.
11. The Quantity of Latent Heat absorbed in Thawing.
12. The Quantity of Latent Heat absorbed in Evaporation.
13. The Law and Rate of Evaporation with regard to Heat.
14. The Law and Rate of the Expansion of Air by Heat.
15. The Quantity of Heat absorbed in the Expansion of Air.
16. The Law and Rate of the Passage of Aqueous Vapour through Air.
17. The Laws of Electricity; its relations to Air and Moisture.
18. The Fluidity, Density, and Elasticity of the Air, by means of
which its vibrations produce Sound.
19. The Fluidity, Density, and Elasticity of the Ether, by means
of which its vibrations produce Light.
2. These are the _data_, the _elements_, as astronomers call
the quantities which determine a planet’s orbit, on which the
mere _inorganic_ part of the universe is constructed. To these,
the constitution of the organic world is adapted in innumerable
points, by laws of which we can trace the results, though we cannot
analyze their machinery. Thus, the vital functions of vegetables
have periods which correspond to the length of the year, and of
the day; their vital powers have forces which correspond to the
force of gravity; the sentient faculties of man are such that
the vibrations of air (within certain limits,) are perceived as
sound, those of ether, as light. And while we are enumerating these
correspondencies, we perceive that there are thousands of others,
and that we can only select a very small number of those where
the relation happens to be most clearly made out or most easily
explained.
Now, in the list of the mathematical _elements_ of the universe
which has just been given, why have we such laws and such
quantities as there occur, and no other? For the most part, the
data there enumerated are independent of each other, and might be
altered separately, so far as the mechanical conditions of the case
are concerned. Some of these data probably depend on each other.
Thus the latent heat of aqueous vapour is perhaps connected with
the difference of the rate of expansion of water and of steam. But
all natural philosophers will, probably, agree, that there must be,
in this list, a great number of things entirely without any mutual
dependence, as the year and the day, the expansion of air and the
expansion of steam. There are, therefore, it appears, a number
of things which, in the structure of the world, might have been
otherwise, and which are what they are in consequence of choice or
of chance. We have already seen, in many of the cases separately,
how unlike chance every thing looks:--that substances, which might
have existed any how, so far as they themselves are concerned,
exist exactly in such a manner and measure as they should, to
secure the welfare of other things:--that the laws are tempered
and fitted together in the only way in which the world could have
gone on, according to all that we can conceive of it. This must,
therefore, be the work of choice; and if so, it cannot be doubted,
of a most wise and benevolent Chooser.
3. The appearance of choice is still further illustrated by the
variety as well as the number of the laws selected. The laws are
unlike one another. Steam certainly expands at a very different
_rate_ from air by the application of heat, probably according to a
different _law_: water expands in freezing, but mercury contracts:
heat travels in a manner quite different through solids and fluids.
Every separate substance has its own density, gravity, cohesion,
elasticity, its relations to heat, to electricity, to magnetism;
besides all its chemical affinities, which form an endless throng
of laws, connecting every one substance in creation with every
other, and different for each pair anyhow taken. Nothing can
look less like a world formed of atoms operating upon each other
according to some universal and inevitable laws, than this does: if
such a system of things be conceivable, it cannot be our system.
We have, it may be, fifty simple substances in the world; each of
which is invested with properties, both of chemical and mechanical
action, altogether different from those of any other substance.
Every portion, however minute, of any of these, possesses all
the properties of the substance. Of each of these substances
there is a certain unalterable quantity in the universe; when
combined, their compounds exhibit new chemical affinities, new
mechanical laws. Who gave these different laws to the different
substances? who proportioned the quantity of each? But suppose
this done. Suppose these substances in existence; in contact, in
due proportion to each other. Is _this_ a world, or at least our
world? No more than the mine and the forest are the ship of war and
the factory. These elements, with their constitution perfect, and
their proportion suitable, are still a mere chaos. They must be put
in their places. They must not be where their own properties would
place them. They must be made to assume a particular arrangement,
or we can have no regular and permanent course of nature. This
arrangement must again have additional peculiarities, or we can
have no organic portion of the world. The millions of millions
of particles which the world contains, must be finished up in
as complete a manner, and fitted into their places with as much
nicety, as the most delicate wheel or spring in a piece of human
machinery. What are the habits of thought to which it can appear
possible that this could take place without design, intention,
intelligence, purpose, knowledge?
In what has just been said, we have spoken only of the constitution
of the inorganic part of the universe. The mechanism, if we may
so call it, of vegetable and animal life, is so far beyond our
comprehension, that though some of the same observations might be
applied to it, we do not dwell upon the subject. We know that in
these processes also, the mechanical and chemical properties of
matter are necessary, but we know too that these alone will not
account for the phenomena of life. There is something more than
these. The lowest stage of vitality and irritability appears to
carry us beyond mechanism, beyond affinity. All that has been said
with regard to the exactness of the adjustments, the combination of
various means, the tendency to continuance, to preservation, is
applicable with additional force to the organic creation, so far
as we can perceive the means employed. These, however, belong to a
different province of the subject, and must be left to other hands.
BOOK II.
COSMICAL ARRANGEMENTS.
When we turn our attention to the larger portions of the universe,
the sun, the planets, and the earth as one of them, the moon and
other satellites, the fixed stars and other heavenly bodies;--the
views which we obtain concerning their mutual relations,
arrangement and movements, are called, as we have already
stated, _cosmical_ views. These views will, we conceive, afford
us indications of the wisdom and care of the Power by which the
objects which we thus consider, were created and are preserved: and
we shall now proceed to point out some circumstances in which these
attributes may be traced.
It has been observed by writers on Natural Theology, that the
arguments for the being and perfections of the Creator, drawn
from cosmical considerations, labour under some disadvantages
when compared with the arguments founded on those provisions
and adaptations which more immediately affect the well-being of
organized creatures. The structure of the solar system has far less
analogy with such machinery as we can construct and comprehend,
than we find in the structure of the bodies of animals, or even in
the causes of the weather. Moreover, we do not see the immediate
bearing of cosmical arrangements on that end which we most readily
acknowledge to be useful and desirable, the support and comfort
of sentient natures. So that, from both causes, the impression of
benevolent design in this case is less striking and pointed than
that which results from the examination of some other parts of
nature.
But in considering the universe, according to the view we have
taken, as a collection of _laws_, astronomy, the science which
teaches us the laws of the motions of the heavenly bodies,
possesses some advantages, among the subjects from which we may
seek to learn the character of the government of the world. For our
knowledge of the laws of the motions of the planets and satellites
is far more complete and exact, far more thorough and satisfactory,
than the knowledge which we possess in any other department of
Natural Philosophy. Our acquaintance with the laws of the solar
system is such, that we can calculate the precise place and motion
of most of its parts at any period, past or future, however
remote; and we can refer the changes which take place in these
circumstances to their proximate cause, the attraction of one mass
of matter to another, acting between all the parts of the universe.
If, therefore, we trace indications of the Divine care, either in
the form of the laws which prevail among the heavenly bodies, or
in the arbitrary quantities which such laws involve; (according
to the distinction explained in the former part of this work;) we
may expect that our examples of such care, though they may be less
numerous and obvious, will be more precise than they can be in
other subjects, where the laws of facts are imperfectly known, and
their causes entirely hid. We trust that this will be found to be
the case with regard to some of the examples which we shall adduce.
CHAPTER I.
_The Structure of the Solar System._
In the cosmical considerations which we have to offer, we shall
suppose the general truths concerning the structure of the solar
system and of the universe, which have been established by
astronomers and mathematicians, to be known to the reader. It is
not necessary to go into much detail on this subject. The five
planets known to the ancients, Mercury, Venus, Mars, Jupiter,
Saturn, revolve round the sun, at different distances, in orbits
nearly circular, and nearly in one plane. Between Venus and Mars,
our Earth, herself one of the planets, revolves in like manner.
Beyond Saturn, Uranus has been discovered describing an orbit of
the same kind; and between Mars and Jupiter, four smaller bodies
perform their revolutions in orbits somewhat less regular than
the rest. These planets are all nearly globular, and all revolve
upon their axis. Some of them are accompanied by satellites, or
attendant bodies which revolve about them; and these bodies also
have their orbits nearly circular, and nearly in the same plane as
the others. Saturn’s ring is a solitary example, so far as we know,
of such an appendage to a planet.
These circular motions of the planets round the sun, and of the
satellites round their primary planets, are all kept going by the
_attraction_ of the respective central bodies, which restrains the
corresponding revolving bodies from flying off. It is perhaps not
very easy to make this operation clear to common apprehension. We
cannot illustrate it by a comparison with any machine of human
contrivance and fabrication: in such machines every thing goes
on by contact and impulse: pressure, and force of all kinds, is
exercised and transferred from one part to another, by means of a
material connexion; by rods, ropes, fluids, gases. In the machinery
of the universe there is, so far as we know, no material connexion
between the parts which act on each other. In the solar system no
part touches or drives another: all the bodies affect each other
_at a distance_, as the magnet affects the needle. The production
and regulation of such effects, if attempted by our mechanicians,
would require great skill and nicety of adjustment; but our artists
have not executed any examples of this sort of machinery, by
reference to which we can illustrate the arrangements of the solar
system.
Perhaps the following comparison may serve to explain the kind of
adjustments of which we shall have to speak. If there be a wide
shallow round basin of smooth marble, and if we take a smooth ball,
as a billiard ball or a marble pellet, and throw it along the
surface of the inside of the basin, the ball will generally make
many revolutions round the inside of the bowl, gradually tending to
the bottom in its motion. The gradual diminution of the motion, and
consequent tendency of the ball to the bottom of the bowl, arises
from the friction; and in order to make the motion correspond to
that which takes place through the action of a central force,
we must suppose this friction to be got rid of. In this case,
the ball, once set a going, would run round the basin for ever,
describing either a circle, or various kinds of ovals, according to
the way in which it was originally thrown; whether quick or slow,
and whether more or less obliquely along the surface.
Such a motion would be capable of the same kind of variety, and the
same sort of adjustments, as the motion of a body revolving about
a larger one by means of a central force. Perhaps the reader may
understand what kind of adjustments these are, by supposing such a
bowl and ball to be used for a game of skill. If the object of the
players be to throw the pellet along the surface of the basin, so
that after describing its curved path it shall pass through a small
hole in a barrier at some distance from the starting point, it will
easily be understood that some nicety in the regulation of the
force and direction with which the ball is thrown will be necessary
for success. In order to obtain a better image of the solar system,
we must suppose the basin to be very large and the pellet very
small. And it will easily be understood that as many pellets as
there are planets might run round the bowl at the same time with
different velocities. Such a contrivance might form a _planetarium_
in which the mimic planets would be regulated by the laws of motion
as the real planets are; instead of being carried by wires and
wheels, as is done in such machines of the common construction:
and in this planetarium the tendency of the planets to the sun is
replaced by the tendency of the representative pellets to run down
the slope of the bowl. We shall refer again to this basin, thus
representing the solar system with its loose planetary balls.
CHAPTER II.
_The Circular Orbits of the Planets round the Sun._
The orbit which the earth describes round the sun is very nearly
a circle: the sun is about one thirtieth nearer to us in winter
than in summer. This nearly circular form of the orbit, on a little
consideration, will appear to be a remarkable circumstance.
Supposing the attraction of a planet towards the sun to exist, if
the planet were put in motion in any part of the solar system, it
would describe about the sun an orbit _of some kind_; it might
be a long oval, or a shorter oval, or an exact circle. But if
we suppose the result left to chance, the chances are infinitely
against the last mentioned case. There is but one circle; there
are an infinite number of ovals. Any original impulse would give
some oval, but only one particular impulse, determinate in velocity
and direction, will give a circle. If we suppose the planet to be
originally _projected_, it must be projected perpendicularly to
its distance from the sun, and with a certain precise velocity, in
order that the motion may be circular.
In the basin to which we have compared the solar system, the
adjustment requisite to produce circular motion would require us
to project our pellet so that after running half round the surface
it should touch a point exactly at an equal distance from the
centre, on the other side, passing neither too high nor too low.
And the pellet, it may be observed, should be in size only one
ten thousandth part of the distance from the centre, to make the
dimensions correspond with the cast of the earth’s orbit. If the
mark were set up and hit, we should hardly attribute the result to
chance.
The earth’s orbit, however, is not exactly a circle. The mark is
not precisely a single point, but is a space of the breadth of one
thirtieth of the distance from the centre. Still this is much too
near an agreement with the circle to be considered as the work of
chance. The chances were great against the ball passing so nearly
at the same distance, for there were twenty-nine equal spaces
through which it might have gone, between the mark and the centre,
and an indefinite number outside the mark.
But it is not the earth’s orbit alone which is nearly a circle:
the rest of the planets also approach very nearly to that form:
Venus more nearly still than the earth: Jupiter, Saturn, and Uranus
have a difference of about one tenth, between their greatest and
least distances from the sun: Mars has his extreme distances in the
proportion of five to six nearly; and Mercury in the proportion of
two to three. The last mentioned case is a considerable deviation,
and two of the small planets which lie between Mars and Jupiter,
namely Juno and Pallas, exhibit an inequality somewhat greater
still; but the smallness of these bodies, and other circumstances,
make it probable that there may be particular causes for the
exception in their case. The orbits of the satellites of the Earth,
of Jupiter and of Saturn, are also nearly circular.
Taking the solar system altogether, the regularity of its structure
is very remarkable. The diagram which represents the orbits of the
planets might have consisted of a number of ovals, narrow and wide
in all degrees, intersecting and interfering with each other in
all directions. The diagram does consist, as all who have opened a
book of astronomy know, of a set of figures which appear at first
sight concentric circles, and which are very nearly so; no where
approaching to any crossing or interfering, except in the case of
the small planets, already noticed as irregular. No one, looking at
this common diagram, can believe that the orbits were made to be
so nearly circles by chance; any more than he can believe that a
target, such as archers are accustomed to shoot at, was painted in
concentric circles by the accidental dashes of a brush in the hands
of a blind man.
The regularity, then, of the solar system excludes the notion of
accident in the arrangement of the orbits of the planets. There
must have been an express adjustment to produce this circular
character of the orbits. The velocity and direction of the motion
of each planet must have been subject to some original regulation;
or, as it is often expressed, the projectile force must have been
accommodated to the centripetal force. This once done, the motion
of each planet, taken by itself, would go on for ever, still
retaining its circular character, by the laws of motion.
If some original cause adjusted the orbits of the planets to
their circular form and regular arrangement, we can hardly avoid
including in our conception of this cause, the intention and will
of a Creating Power. We shall consider this argument more fully
in a succeeding chapter; only observing here, that the presiding
Intelligence, which has selected and combined the properties of the
organic creation, so that they correspond so remarkably with the
arbitrary quantities of the system of the universe, may readily
be conceived also to have selected the arbitrary velocity and
direction of each planet’s motion, so that the adjustment should
produce a close approximation to a circular motion.
We have argued here only from the _regularity_ of the solar
system; from the selection of the single symmetrical case and the
rejection of all the unsymmetrical cases. But this subject may be
considered in another point of view. The system thus selected is
not only regular and symmetrical, but also it is, so far as we can
judge, the only one which would answer the purpose of the earth,
perhaps of the other planets, as the seat of animal and vegetable
life. If the earth’s orbit were more eccentric, as it is called,
if for instance the greatest and least distances were as three
to one, the inequality of heat at two seasons of the year would
be destructive to the existing species of living creatures. A
circular, or nearly circular, orbit, is the only case in which we
can have a course of seasons such as we have at present, the only
case in which the climates of the northern and southern hemispheres
are nearly the same; and what is more clearly important, the only
case in which the character of the seasons would not vary from
century to century. For if the eccentricity of the earth’s orbit
were considerable, the difference of heat at different seasons,
arising from the different distances of the sun, would be combined
with the difference, now the only considerable one, which depends
on the position of the earth’s axis. And as by the motion of
the _perihelion_, or place of the nearest distance of the earth
to the sun, this nearest distance would fall in different ages
at different parts of the year, the whole distribution of heat
through the year would thus be gradually subverted. The summer and
winter of the _tropical_ year, as we have it now, being combined
with the heat and cold of the _anomalistic_ year, a period of
different length, the difference of the two seasons might sometimes
be neutralized altogether, and at other times exaggerated by the
accumulation of the inequalities, so as to be intolerable.
The circular form of the orbit therefore, which, from its unique
character, appears to be chosen with _some_ design, from its
effects on the seasons appears to be chosen with this design,
so apparent in other parts of creation, of securing the welfare
of organic life, by a steadfast and regular order of the solar
influence upon the planet.
CHAPTER III.
_The Stability of the Solar System._
There is a consequence resulting from the actual structure of the
solar system, which has been brought to light by the investigations
of mathematicians concerning the cause and laws of its motions, and
which has an important bearing on our argument. It appears that the
arrangement which at present obtains is precisely that which is
necessary to secure the _stability_ of the system. This point we
must endeavour to explain.
If each planet were to revolve round the sun without being affected
by the other planets, there would be a certain degree of regularity
in its motion; and this regularity would continue for ever. But it
appears, by the discovery of the law of universal gravitation,
that the planets do not execute their movements in this insulated
and independent manner. Each of them is acted on by the attraction
of all the rest. The Earth is constantly drawn by Venus, by Mars,
by Jupiter, bodies of various magnitudes, perpetually changing
their distances and positions with regard to the earth; the Earth
in return is perpetually drawing these bodies. What, in the course
of time, will be the result of this mutual attraction?
All the planets are very small compared with the sun, and therefore
the derangement which they produce in the motion of one of their
number will be very small in the course of one revolution. But this
gives us no security that the derangement may not become very large
in the course of many revolutions. The cause acts perpetually,
and it has the whole extent of time to work in. Is it not easily
conceivable then that in the lapse of ages the derangements of
the motions of the planets may accumulate, the orbits may change
their form, their mutual distances may be much increased or much
diminished? Is it not possible that these changes may go on without
limit, and end in the complete subversion and ruin of the system?
If, for instance, the result of this mutual gravitation should be
to increase considerably the eccentricity of the earth’s orbit,
that is to make it a longer and longer oval; or to make the moon
approach perpetually nearer and nearer the earth every revolution;
it is easy to see that in the one case our year would change its
character, as we have noticed in the last section; in the other,
our satellite might finally fall to the earth, which must of
course bring about a dreadful catastrophe. If the positions of
the planetary orbits, with respect to that of the earth, were to
change much, the planets might sometimes come very near us, and
thus exaggerate the effects of their attraction beyond calculable
limits. Under such circumstances, we might have “years of unequal
length, and seasons of capricious temperature, planets and moons of
portentous size and aspect, glaring and disappearing at uncertain
intervals;” tides like deluges, sweeping over whole continents;
and, perhaps, the collision of two of the planets, and the
consequent destruction of all organization on both of them.
Nor is it, on a common examination of the history of the solar
system, at all clear that there is no tendency to indefinite
derangement. The fact really is, that changes are taking place
in the motions of the heavenly bodies, which have gone on
progressively from the first dawn of science. The eccentricity
of the earth’s orbit has been diminishing from the earliest
observations to our times. The moon has been moving quicker and
quicker from the time of the first recorded eclipses, and is now
in advance, by about four times her own breadth, of what her place
would have been if it had not been affected by this acceleration.
The obliquity of the ecliptic also is in a state of diminution, and
is now about two-fifths of a degree less than it was in the time
of Aristotle. Will these changes go on without limit or reaction?
If so, we tend by natural causes to a termination of the present
system of things: If not, by what adjustment or combination are we
secured from such a tendency? Is the system _stable_, and if so,
what is the condition on which its stability depends?
To answer these questions is far from easy. The mechanical problem
which they involve is no less than this;--Having given the
directions and velocities with which about thirty bodies are moving
at one time, to find their places and motions after any number of
ages; each of the bodies, all the while, attracting all the others,
and being attracted by them all.
It may readily be imagined that this is a problem of extreme
complexity, when it is considered that every new _configuration_
or arrangement of the bodies will give rise to a new amount of
action on each; and every new action to a new configuration.
Accordingly, the mathematical investigation of such questions as
the above was too difficult to be attempted in the earlier periods
of the progress of Physical Astronomy. Newton did not undertake to
demonstrate either the stability or the instability of the system.
The decision of this point required a great number of preparatory
steps and simplifications, and such progress in the invention
and improvement of mathematical methods, as occupied the best
mathematicians of Europe for the greater part of last century.
But, towards the end of that time, it was shown by Lagrange and
Laplace that the arrangements of the solar system are stable: that
in the long run, the orbits and motions remain unchanged; and that
the changes in the orbits, which take place in shorter periods,
never transgress certain very moderate limits. Each orbit undergoes
deviations on this side and on that of its average state; but these
deviations are never very great, and it finally recovers from them,
so that the average is preserved. The planets produce perpetual
perturbations in each other’s motions, but these perturbations
are not indefinitely progressive, they are periodical: they reach
a _maximum_ value and then diminish. The periods which this
restoration requires are, for the most part, enormous; not less
than thousands, and, in some instances, millions of years; and
hence it is, that some of these apparent derangements have been
going on in the same direction since the beginning of the history
of the world. But the restoration is in the sequel as complete as
the derangement; and in the meantime the disturbance never attains
a sufficient amount seriously to alter the adaptations of the
system.[17]
The same examination of the subject by which this is proved, points
out also the conditions on which this stability depends. “I have
succeeded in demonstrating,” says Laplace, “that whatever be the
masses of the planets, in consequence of the fact that they all
move in the same direction, in orbits of small eccentricity, and
slightly inclined to each other--their secular inequalities are
periodical and included within narrow limits; so that the planetary
system will only oscillate about a mean state, and will never
deviate from it except by a very small quantity. The ellipses of
the planets have been, and always will be, nearly circular. The
ecliptic will never coincide with the equator, and the entire
extent of the variation in its inclination cannot exceed three
degrees.”
There exists, therefore, it appears, in the solar system, a
provision for the permanent regularity of its motions; and this
provision is found in the fact that the orbits of the planets are
nearly circular, and nearly in the same plane, and the motions all
in the same direction, namely, from west to east.[18]
Now is it probable that the occurrence of these conditions of
stability in the disposition of the solar system is the work of
chance? Such a supposition appears to be quite inadmissible. Any
one of the orbits might have had any eccentricity.[19] In that
of Mercury, where it is much the greatest, it is only one-fifth.
How came it to pass that the orbits were not more elongated? A
little more or a little less velocity in their original motions
would have made them so. They might have had any inclination to
the ecliptic from _no_ degrees to 90 degrees. Mercury, which again
deviates most widely, is inclined 7¾ degrees, Venus 3¾, Saturn
2¾, Jupiter 1½, Mars 2. How came it that their motions are thus
contained within such a narrow strip of the sky? One, or any number
of them, might have moved from east to west: none of them does so.
And these circumstances, which appear to be, each in particular,
requisite for the stability of the system and the smallness of its
disturbances, are all found in combination. Does not this imply
both clear purpose and profound skill?
It is difficult to convey an adequate notion of the extreme
complexity of the task thus executed. A number of bodies, all
attracting each other, are to be projected in such a manner that
their revolutions shall be permanent and stable, their mutual
perturbations always small. If we return to the basin with its
rolling balls, by which we before represented the solar system, we
must complicate with new conditions the trial of skill which we
supposed. The problem must now be to project at once seven such
balls, all connected by strings which influence their movements, so
that each may hit its respective mark. And we must further suppose,
that the marks are to be hit after many thousand revolutions of the
balls. No one will imagine that this could be done by accident.
In fact it is allowed by all those who have considered this
subject, that such a coincidence of the existing state with the
mechanical requisites of permanency cannot be accidental. Laplace
has attempted to calculate the probability that it is not the
result of accident. He takes into account, in addition to the
motions which we have mentioned, the revolutions of the satellites
about their primaries, and of the sun and planets about their
axes: and he finds that there is a probability, far higher than
that which we have for the greater part of undoubted historical
events, that these appearances are not the effect of chance. “We
ought, therefore,” he says, “to believe, with at least the same
confidence, that a primitive cause has directed the planetary
motions.”
The solar system is thus, by the confession of all sides,
completely different from any thing which we might anticipate from
the casual operation of its known laws. The laws of motion are no
less obeyed to the letter in the most irregular than in the most
regular motions; no less in the varied circuit of the ball which
flies round a tennis court, than in the going of a clock; no less
in the fantastical jets and leaps which breakers make when they
burst in a corner of a rocky shore, than in the steady swell of the
open sea. The laws of motion alone will not produce the regularity
which we admire in the motions of the heavenly bodies. There must
be an original adjustment of the system on which these laws are
to act; a selection of the arbitrary quantities which they are to
involve; a primitive cause which shall dispose the elements in
due relation to each other, in order that regular recurrence may
accompany constant change; that perpetual motion may be combined
with perpetual stability; that derangements which go on increasing
for thousands or for millions of years may finally cure themselves;
and that the same laws which lead the planets slightly aside from
their paths, may narrowly limit their deviations, and bring them
back from their almost imperceptible wanderings.
If a man does not deny that any possible peculiarity in the
disposition of the planets with regard to the sun could afford
evidence of a controlling and ordering purpose, it seems difficult
to imagine how he could look for evidence stronger than that
which there actually is. Of all the innumerable possible cases of
systems, governed by the existing laws of force and motion, that
one is selected which alone produces such a steadfast periodicity,
such a constant average of circumstances, as are, so far as we can
conceive, necessary conditions for the existence of organic and
sentient life. And this selection is so far from being an obvious
or easily discovered means to this end, that the most profound and
attentive consideration of the properties of space and number, with
all the appliances and aids we can obtain, are barely sufficient to
enable _us_ to see that the end is thus secured, and that it can be
secured in no other way. Surely the obvious impression which arises
from this view of the subject is, that the solar system, with
its adjustments, is the work of an intelligence, who perceives,
as self-evident, those truths, to which we attain painfully and
slowly, and after all imperfectly; who has employed in every part
of creation refined contrivances, which we can only with effort
understand; and who, in innumerable instances, exhibits to us what
we should look upon as remarkable difficulties remarkably overcome,
if it were not that, through the perfection of the provision, the
trace of the difficulty is almost obliterated.
CHAPTER IV.
_The Sun in the Centre._
The next circumstance which we shall notice as indicative of design
in the arrangement of the material portions of the solar system,
is the position of the sun, the source of light and heat, in the
centre of the system. This could hardly have occurred by any
thing which we can call chance. Let it be granted, that the law of
gravitation is established, and that we have a large mass, with
others much smaller in its comparative vicinity. The small bodies
may then move round the larger, but this will do nothing towards
making it a _sun_ to them. Their motions might take place, the
whole system remaining still utterly dark and cold, without day or
summer. In order that we may have something more than this blank
and dead assemblage of moving clods, the machine must be lighted
up and warmed. Some of the advantages of placing the lighting
and warming apparatus in the centre are obvious to us. It is in
this way only that we could have those regular periodical returns
of solar influence, which, as we have seen, are adapted to the
constitution of the living creation. And we can easily conceive,
that there may be other incongruities in a system with a travelling
sun, of which we can only conjecture the nature. No one probably
will doubt that the existing system, with the sun in the centre, is
better than any one of a different kind would be.
Now this lighting and warming by a central sun are something
superadded to the mere mechanical arrangements of the universe.
There is no apparent reason why the largest mass of gravitating
matter should diffuse inexhaustible supplies of light and heat in
all directions, while the other masses are merely passive, with
respect to such influences. There is no obvious connexion between
mass and luminousness, or temperature. No one, probably, will
contend that the materials of our system are necessarily luminous
or hot. According to the conjectures of astronomers, the heat and
light of the sun do not reside in its mass, but in a coating which
lies on its surface. If such a coating were fixed there by the
force of universal gravitation, how could we avoid having a similar
coating on the surface of the earth, and of all the other globes of
the system. If light consist in the vibrations of an ether, which
we have mentioned as a probable opinion, why has the sun alone the
power of exciting such vibrations? If light be the emission of
material particles, why does the sun alone emit such particles?
Similar questions may be asked, with regard to heat, whatever be
the theory we adopt on that subject. Here then we appear to find
marks of contrivance. The sun might become, we will suppose, the
centre of the motions of the planets by mere mechanical causes:
but what caused the centre of their motions to be also the source
of those vivifying influences? Allowing that no interposition was
requisite to regulate the revolutions of the system, yet observe
what a peculiar arrangement in other respects was necessary, in
order that these revolutions might produce days and seasons! The
machine will move of itself, we may grant: but who constructed the
machine, so that its movements might answer the purposes of life?
How was the candle placed upon the candlestick? How was the fire
deposited on the hearth, so that the comfort and well-being of the
family might be secured? Did these too fall into their places by
the casual operation of gravity? And, if not, is there not here
a clear evidence of intelligent design, of arrangement with a
benevolent end?
This argument is urged with great force by Newton himself. In his
first letter to Bentley, he allows that matter might form itself
into masses by the force of attraction. “And thus,” says he, “might
the sun and fixed stars be formed, supposing the matter were of
a lucid nature. But how the matter should divide itself into two
sorts; and that part of it which is fit to compose a shining body
should fall down into one mass, and make a sun; and the rest, which
is fit to compose an opaque body, should coalesce, not into one
great body, like the shining matter, but into many little ones; or
if the sun at first were an opake body like the planets, or the
planets lucid bodies like the sun, how he alone should be changed
into a shining body, whilst all they continue opake; or all they
be changed into opake ones, while he continued unchanged: I do not
think explicable by mere natural causes, but am forced to ascribe
it to the counsel and contrivance of a voluntary Agent.”
CHAPTER V.
_The Satellites._
1. A person of ordinary feelings, who, on a fine moonlight night,
sees our satellite pouring her mild radiance on field and town,
path and moor, will probably not only be disposed to “bless the
useful light,” but also to believe that it was “ordained” for that
purpose;--that the lesser light was made to rule the night as
certainly as the greater light was made to rule the day.
Laplace, however, does not assent to this belief. He observes,
that “some partisans of final causes have imagined that the moon
was given to the earth to afford light during the night:” but he
remarks that this cannot be so, for that we are often deprived at
the same time of the light of the sun and the moon; and he points
out how the moon might have been placed so as to be always “full.”
That the light of the moon affords, _to a certain extent_, a
supplement to the light of the sun, will hardly be denied. If
we take man in a condition in which he uses artificial light
scantily only, or not at all, there can be no doubt that the
moonlight nights are for him a very important addition to the time
of daylight. And as a small proportion only of the whole number
of nights are without some portion of moonlight, the fact that
sometimes both luminaries are invisible very little diminishes the
value of this advantage. Why we have not more moonlight, either in
duration or in quantity, is an inquiry which a philosopher could
hardly be tempted to enter upon, by any success which has attended
previous speculations of a similar nature. Why should not the moon
be ten times as large as she is? Why should not the pupil of man’s
eye be ten times as large as it is, so as to receive more of the
light which does arrive? We do not conceive that our inability
to answer the latter question prevents our knowing that the eye
was made for seeing: nor does our inability to answer the former,
disturb our persuasion that the moon was made to give light upon
the earth.
Laplace suggests that if the moon had been placed at a certain
distance beyond the earth, it would have revolved about the sun in
the same time as the earth does, and would have always presented
to us a full moon. For this purpose it must have been about four
times as far from us as it really is; and would therefore, other
things remaining unchanged, have only been _one sixteenth_ as
large to the eye as our present full moon. We shall not dwell on
the discussion of this suggestion, for the reason just intimated.
But we may observe that in such a system as Laplace proposes,
it is not yet proved, we believe, that the arrangement would be
stable under the influence of the disturbing forces. And we may add
that such an arrangement, in which the motion of one body has a
_co-ordinate_ reference to two others, as the motion of the moon on
this hypothesis would have to the sun and the earth, neither motion
being subordinate to the other, is contrary to the whole known
analogy of cosmical phenomena, and therefore has no claim to our
notice as a subject of discussion.
2. In turning our consideration to the satellites of the other
planets of our system, there is one fact which immediately arrests
our attention;--the number of such attendant bodies appears to
increase as we proceed to planets farther and farther from the
sun. Such at least is the general rule. Mercury and Venus, the
planets nearest the sun, have no such attendants: the Earth has
one. Mars, indeed, who is still farther removed, has none; nor
have the minor planets, Juno, Vesta, Ceres, Pallas; so that the
rule is only approximately verified. But Jupiter, who is at five
times the earth’s distance, has four satellites; and Saturn, who
is again at a distance nearly twice as great, has seven, besides
that most extraordinary phenomenon his ring, which, for purposes of
illumination, is equivalent to many thousand satellites. Of Uranus
it is difficult to speak, for his great distance renders it almost
impossible to observe the smaller circumstances of his condition.
It does not appear at all probable that he has a ring, like Saturn;
but he has at least five satellites which are visible to us, at the
enormous distance of nine hundred millions of miles; and we believe
that the astronomer will hardly deny that he may possibly have
thousands of smaller ones circulating about him.
But leaving conjecture, and taking only the ascertained cases
of Venus, the Earth, Jupiter, and Saturn, we conceive that a
person of common understanding will be strongly impressed with
the persuasion that the satellites are placed in the system
with a view to compensate for the diminished light of the sun
at greater distances. The smaller planets, Juno, Vesta, Ceres,
and Pallas, differ from the rest in so many ways, and suggest so
many conjectures of reasons for such differences, that we should
almost expect to find them exceptions to such a rule. Mars is a
more obvious exception. Some persons might conjecture from his
case, that the arrangement itself, like other useful arrangements,
has been brought about by some wider law which we have not yet
detected. But whether or not we entertain such a guess, (it can be
nothing more,) we see in other parts of creation, so many examples
of apparent exceptions to rules, which are afterwards found to be
explained, or provided for by particular contrivances, that no one,
familiar with such contemplations, will, by one anomaly, be driven
from the persuasion that the end which the arrangements of the
satellites seem suited to answer is really one of the ends of their
creation.
CHAPTER VI.
_The Stability of the Ocean._
What is meant by the stability of the ocean may perhaps be
explained by means of the following illustration. If we suppose
the whole globe of the Earth to be composed of water, a sphere
of cork, immersed in any part of it, would come to the surface
of the water, except it were placed exactly at the centre of the
earth; and even if it were the slightest displacement of the cork
sphere would end in its rising and floating. This would be the case
whatever were the size of the cork sphere, and even if it were so
large as to leave comparatively little room for the water; and the
result would be nearly the same, if the cork sphere, when in its
central position, had on its surface prominences which projected
above the surface of the water. Now this brings us to the case in
which we have a globe resembling our present earth, composed like
it of water and of a solid centre, with islands and continents,
but having these solid parts all made of cork. And it appears by
the preceding reasoning, that in this case, if there were any
disturbance either of the solid or fluid parts, the solid parts
would rise from the centre of the watery sphere as far as they
could: that is, all the water would run to one side and leave the
land on the other. Such an ocean would be in _unstable_ equilibrium.
Now a question naturally occurs, is the equilibrium of our present
ocean of this unstable kind, or is it stable? The sea, after its
most violent agitations, appears to return to its former state of
repose; but may not some extraordinary cause produce in it some
derangement which may go on increasing till the waters all rush one
way, and thus drown the highest mountains? And if we are safe from
this danger, what are the conditions by which we are so secured?
The illustration which we have employed obviously suggests the
answer to this question; namely, that the equilibrium is unstable,
so long as the solid parts are of such a kind as to float in the
fluid parts; and of course we should expect that the equilibrium
will be stable whenever the contrary is the case, that is, when
the solid parts of the earth are of greater specific gravity than
the sea. A more systematic mathematical calculation has conducted
Laplace to a demonstration of this result.
The mean specific gravity of the earth appears to be about _five_
times that of water, so that the condition of the stability of the
ocean is abundantly fulfilled. And the provision by which this
stability is secured was put in force through the action of those
causes, whatever they were, which made the density of the solid
materials and central parts of the earth greater than the density
of the incumbent fluid.
When we consider, however, the manner in which the wisdom of the
Creator, even in those cases in which his care is most apparent,
as in the structure of animals, works by means of intermediate
causes and general laws, we shall not be ready to reject all belief
of an end in such a case as this, merely because the means are
mechanical agencies. Laplace says, “in virtue of gravity, the most
dense of the strata of the earth are those nearest to the centre;
and thus the mean density exceeds that of the waters which cover
it; which suffices to secure the stability of the equilibrium of
the seas, and to put a bridle upon the fury of the waves.” This
statement, if exact, would not prove that He who subjected the
materials of the earth to the action of gravity did not _intend_
to restrain the rage of the waters: but the statement is not true
in fact. The lower strata, so far as man has yet examined, are
very far from being constantly, or even generally, heavier than
the superincumbent ones. And certainly solidification by no means
implies a greater density than fluidity: the density of Jupiter
is one fourth, that of Saturn less than one seventh, of that of
the earth. If an ocean of water were poured into the cavities upon
the surface of Saturn, its equilibrium would _not_ be stable. It
would leave its bed on one side of the globe; and the planet would
finally be composed of one hemisphere of water and one of land.
If the Earth had an ocean of a fluid six times as heavy as water,
(quicksilver is thirteen times as heavy,) we should have, in like
manner, a dry and a fluid hemisphere. Our inland rivers would
probably never be able to reach the shores, but would be dried up
on their way, like those which run in torrid desarts; perhaps the
evaporation from the ocean would never reach the inland mountains,
and we should have no rivers at all. Without attempting to imagine
the details of such a condition, it is easy to see, that to secure
the existence of a different one is an end which is in harmony with
all that we see of the preserving care displayed in the rest of
creation.[20]
CHAPTER VII.
_The Nebular Hypothesis._
We have referred to Laplace, as a profound mathematician, who has
strongly expressed the opinion, that the arrangement by which
the stability of the solar system is secured is not the result
of chance; that “_a primitive cause_ has directed the planetary
motions.” This author, however, having arrived, as we have done,
at this conviction, does not draw from it the conclusion which has
appeared to us so irresistible, that “the admirable arrangement
of the solar system cannot but be the work of an intelligent and
most powerful being.” He quotes these expressions, which are
those of Newton, and points at them as instances where that great
philosopher had deviated from the method of true philosophy.
He himself proposes an hypothesis concerning the nature of the
_primitive cause_ of which he conceives the existence to be thus
probable: and this hypothesis, on account of the facts which it
attempts to combine, the view of the universe which it presents,
and the eminence of the person by whom it is propounded, deserves
our notice.
1. Laplace conjectures that in the original condition of the solar
system, the sun revolved upon his axis, surrounded by an atmosphere
which, in virtue of an excessive heat, extended far beyond the
orbits of all the planets, the planets as yet having no existence.
The heat gradually diminished, and as the solar atmosphere
contracted by cooling, the rapidity of its rotation increased by
the laws of rotatory motion, and an exterior zone of vapour was
detached from the rest, the central attraction being no longer able
to overcome the increased centrifugal force. This zone of vapour
might in some cases retain its form, as we see it in Saturn’s
ring; but more usually the ring of vapour would break into several
masses, and these would generally coalesce into one mass, which
would revolve about the sun. Such portions of the solar atmosphere,
abandoned successively at different distances, would form “planets
in the state of vapour.” These planets, it appears from mechanical
considerations, would have each its rotatory motion, and as the
cooling of the vapour still went on, would each produce a planet,
which might have satellites and rings, formed from the planet in
the same manner as the planets were formed from the atmosphere of
the sun.
It may easily be conceived that all the primary motions of a system
so produced would be nearly circular, nearly in the plane of the
original equator of the solar rotation, and in the direction of
that rotation. Reasons are offered also to show that the motions
of the satellites thus produced and the motions of rotation of the
planets must be in the same direction. And thus it is held that the
hypothesis accounts for the most remarkable circumstances in the
structure of the solar system: namely, the motions of the planets
in the same direction, and almost in the same plane; the motions
of the satellites in the same direction as those of the planets;
the motions of rotation of these different bodies still in the same
direction as the other motions, and in planes not much different;
the small eccentricity of the orbits of the planets, upon which
condition, along with some of the preceding ones, the stability of
the system depends; and the position of the source of light and
heat in the centre of the system.
It is not necessary for the purpose, nor suitable to the plan
of the present treatise, to examine, on physical grounds, the
probability of the above hypothesis. It is proposed by its author,
with great diffidence, as a conjecture only. We might, therefore,
very reasonably put off all discussion of the bearings of this
opinion upon our views of the government of the world, till the
opinion itself should have assumed a less indistinct and precarious
form. It can be no charge against our doctrines, that there is
a difficulty in reconciling with them arbitrary guesses and
half-formed theories. We shall, however, make a few observations
upon this _nebular hypothesis_, as it may be termed.
2. If we grant, for a moment, the hypothesis, it by no means proves
that the solar system was formed without the intervention of
intelligence and design. It only transfers our view of the skill
exercised, and the means employed, to another part of the work.
For, how came the sun and its atmosphere to have such materials,
such motions, such a constitution, that these consequences
followed from their primordial condition? How came the parent
vapour thus to be capable of coherence, separation, contraction,
solidification? How came the laws of its motion, attraction,
repulsion, condensation, to be so fixed, as to lead to a beautiful
and harmonious system in the end? How came it to be neither too
fluid nor too tenacious, to contract neither too quickly nor too
slowly, for the successive formation of the several planetary
bodies? How came that substance, which at one time was a luminous
vapour, to be at a subsequent period, solids and fluids of many
various kinds? What but design and intelligence prepared and
tempered this previously existing element, so that it should by its
natural changes produce such an orderly system?
And if in this way we suppose a planet to be produced, what sort
of a body would it be?--something, it may be presumed, resembling
a large meteoric stone. How comes this mass to be covered with
motion and organization, with life and happiness? What primitive
cause stocked it with plants and animals, and produced all the
wonderful and subtle contrivances which we find in their structure,
all the wide and profound mutual dependencies which we trace in
their economy? Was man, with his thought and feeling, his powers
and hopes, his will and conscience, also produced as an ultimate
result of the condensation of the solar atmosphere? Except we allow
a prior purpose and intelligence presiding over this material
“primitive cause,” how irreconcilable is it with the evidence which
crowds in upon us from every side!
3. In the next place, we may observe concerning this hypothesis,
that it carries us back to the beginning of the present system
of things; but that it is impossible for our reason to stop at
the point thus presented to it. The sun, the earth, the planets,
the moons were brought into their present order out of a previous
state, and, as is supposed in the theory, by the natural operation
of laws. But how came that previous state to exist? We are
compelled to suppose that it, in like manner, was educed from a
still prior state of things; and this, again, must have been the
result of a condition prior still. Nor is it possible for us to
find, in the tenets of the nebular hypothesis, any resting place or
satisfaction for the mind. The same reasoning faculty, which seeks
for the origin of the present system of things, and is capable
of assenting to, or dissenting from the hypothesis propounded
by Laplace as an answer to this inquiry, is necessarily led to
seek, in the same manner, for the origin of any previous system
of things, out of which the present may appear to have grown: and
must pursue this train of inquiries unremittingly, so long as the
answer which it receives describes a mere assemblage of matter and
motion; since it would be to contradict the laws of matter and the
nature of motion, to suppose such an assemblage to be the _first_
condition.
The reflection just stated, may be illustrated by the further
consideration of the Nebular Hypothesis. This opinion refers us,
for the origin of the solar system, to a sun surrounded with an
atmosphere of enormously elevated temperature, revolving and
cooling. But as we ascend to a still earlier period, what state
of things are we to suppose?--a still higher temperature, a still
more diffused atmosphere. Laplace conceives that, in its primitive
state, the sun consisted in a diffused luminosity so as to resemble
those nebulæ among the fixed stars, which are seen by the aid of
the telescope, and which exhibit a nucleus, more or less brilliant,
surrounded by a cloudy brightness. “This anterior state was itself
preceded by other states, in which the nebulous matter was more and
more diffuse, the nucleus being less and less luminous. We arrive,”
Laplace says, “in this manner, at a nebulosity so diffuse, that its
existence could scarcely be suspected.”
“Such is,” he adds, “in fact, the first state of the nebulæ which
Herschel carefully observed by means of his powerful telescopes.
He traced the progress of condensation, not indeed on one nebula,
for this progress can only become perceptible to us in the course
of centuries; but in the assemblage of nebulæ; much in the same
manner as in a large forest we may trace the growth of trees among
the examples of different ages which stand side by side. He saw in
the first place the nebulous matter dispersed in patches, in the
different parts of the sky. He saw in some of these patches this
matter feebly condensed round one or more faint nuclei. In other
nebulæ, these nuclei were brighter in proportion to the surrounding
nebulosity; when by a further condensation the atmosphere of each
nucleus becomes separate from the others, the result is multiple
nebulous stars, formed by brilliant nuclei very near each other,
and each surrounded by an atmosphere: sometimes the nebulous matter
condensing in a uniform manner has produced nebulous systems
which are called _planetary_. Finally, a still greater degree of
condensation transforms all these nebulous systems into stars. The
nebulæ, classed according to this philosophical view, indicate with
extreme probability their future transformation into stars, and
the anterior nebulous condition of the stars which now exist.”
It appears then that the highest point to which this series of
conjectures can conduct us, is, “an extremely diffused nebulosity,”
attended, we may suppose, by a far higher degree of heat, than that
which, at a later period of the hypothetical process, keeps all the
materials of our earth and planets in a state of vapour. Now is it
not impossible to avoid asking, whence was this light, this heat,
this diffusion? How came the laws which such a state implies, to be
already in existence? Whether light and heat produce their effects
by means of fluid vehicles or otherwise, they have complex and
varied laws which indicate the existence of some subtle machinery
for their action. When and how was this machinery constructed?
Whence too that enormous expansive power which the nebulous matter
is supposed to possess? And if, as would seem to be supposed in
this doctrine, all the material ingredients of the earth existed
in this diffuse nebulosity, either in the state of vapour, or in
some state of still greater expansion, whence were they and their
properties? how came there to be of each simple substance which
now enters into the composition of the universe, just so much and
no more? Do we not, far more than ever, require an origin of this
origin? an explanation of this explanation? Whatever may be the
merits of the opinion as a physical hypothesis, with which we do
not here meddle, can it for a moment prevent our looking beyond
the hypothesis, to a First Cause, an Intelligent Author, an origin
proceeding from free volition, not from material necessity?
But again: let us ascend to the highest point of the hypothetical
progression: let us suppose the nebulosity diffused throughout
all space, so that its course of running into patches is not yet
begun. How are we to suppose it distributed? Is it equably diffused
in every part? clearly not; for if it were, what should cause it
to gather into masses, so various in size, form and arrangement?
The separation of the nebulous matter into distinct nebulæ implies
necessarily some original inequality of distribution; some
determining circumstances in its primitive condition. Whence were
these circumstances? this inequality? we are still compelled to
seek some ulterior agency and power.
Why must the primeval condition be one of change at all? Why should
not the nebulous matter be equably diffused throughout space, and
continue for ever in its state of equable diffusion, as it must
do, from the absence of all cause to determine the time and manner
of its separation? why should this nebulous matter grow cooler and
cooler? why should it not retain for ever the same degree of heat,
whatever heat be? If heat be a fluid, if to cool be to part with
this fluid, as many philosophers suppose, what becomes of the fluid
heat of the nebulous matter, as the matter cools down? Into what
unoccupied region does it find its way?
Innumerable questions of the same kind might be asked, and the
conclusion to be drawn is, that every new physical theory which
we include in our view of the universe, involves us in new
difficulties and perplexities, if we try to erect it into an
ultimate and final account of the existence and arrangement of
the world in which we live. With the evidence of such theories,
considered as scientific generalizations of ascertained facts,
with their claims to a place in our natural philosophy, we have
here nothing to do. But if they are put forwards as a disclosure
of the ultimate cause of that which occurs, and as superseding
the necessity of looking further or higher; if they claim a place
in our Natural Theology, as well as our Natural Philosophy;
we conceive that their pretensions will not bear a moment’s
examination.
Leaving then to other persons and to future ages to decide upon the
scientific merits of the nebular hypothesis, we conceive that the
final fate of this opinion cannot, in sound reason, affect at all
the view which we have been endeavouring to illustrate;--the view
of the universe as the work of a wise and good Creator. Let it be
supposed that the point to which this hypothesis leads us, is the
ultimate point of physical science: that the farthest glimpse we
can obtain of the material universe by our natural faculties, shows
it to us occupied by a boundless abyss of luminous matter: still we
ask, how space came to be thus occupied, how matter came to be thus
luminous? If we establish by physical proofs, that the first fact
which can be traced in the history of the world, is that “there
was light;” we shall still be led, even by our natural reason,
to suppose that before this could occur, “God said, let there be
light.”
CHAPTER VIII.
_The Existence of a Resisting Medium in the Solar System._
The question of a _plenum_ and a _vacuum_ was formerly much
debated among those who speculated concerning the constitution of
the universe; that is, they disputed whether the celestial and
terrestrial spaces are absolutely full, each portion being occupied
by some matter or other; or whether there are, between and among
the material parts of the world, empty spaces free from all matter,
however rare. This question was often treated by means of abstract
conceptions and _à priori_ reasonings; and was sometimes considered
as one in which the result of the struggle between rival systems of
philosophy, the Cartesian and Newtonian for instance, was involved.
It was conceived by some that the Newtonian doctrine of the motions
of the heavenly bodies, according to mechanical laws, required
that the space in which they moved should be, absolutely and
metaphysically speaking, a vacuum.
This, however, is not necessary to the truth of the Newtonian
doctrines, and does not appear to have been intended to be asserted
by Newton himself. Undoubtedly, according to his theory, the
motions of the heavenly bodies were calculated _on the supposition_
that they do move in a space void of any resisting fluid; and the
comparison of the places so calculated with the places actually
observed, (continued for a long course of years, and tried in
innumerable cases,) did not show any difference which implied the
existence of a resisting fluid. The Newtonian, therefore, was
justified in asserting that _either_ there was no such fluid, _or_
that it was so thin and rarefied, that no phenomenon yet examined
by astronomers was capable of betraying its effects.
This was all that the Newtonian needed or ought to maintain; for
his philosophy, founded altogether upon observation, had nothing to
do with abstract possibilities and metaphysical necessities. And in
the same manner in which observation and calculation thus showed
that there could be none but a very rare medium pervading the solar
system, it was left open to observation and calculation to prove
that there was such a medium, if any facts could be discovered
which offered suitable evidence.
Within the last few years, facts have been observed which show,
in the opinion of some of the best mathematicians of Europe, that
such a very rare medium does really occupy the spaces in which the
planets move; and it may be proper and interesting to consider the
bearing of this opinion upon the views and arguments which we have
had here to present.
1. Reasons might be offered, founded on the universal diffusion of
light and on other grounds, for believing that the planetary spaces
cannot be entirely free from matter of some kind; and wherever
matter is, we should expect resistance. But the facts which have
thus led astronomers to the conviction that such a resisting
medium really exists, are certain circumstances occurring in the
motion of a body revolving round the sun, which is now usually
called _Encke’s comet_. This body revolves in a very eccentric
or oblong orbit, its greatest or aphelion distance from the sun,
and its nearest, or perihelion distance, being in the proportion
of more than ten to one. In this respect it agrees with other
comets; but its time of revolution about the sun is much less
than that of the comets which have excited most notice; for while
they appear only at long intervals of years, the body of which we
are now speaking returns to its perihelion every twelve hundred
and eight days, or in about three years and one-third. Another
observable circumstance in this singular body, is its extreme
apparent tenuity: it appears as a loose indefinitely formed speck
of vapour, through which the stars are visible with no perceptible
diminution of their brightness. This body was first seen by
Mechain and Messier, in 1786,[21] but they obtained only two
observations, whereas three, at least, are requisite to determine
the path of a heavenly body. Miss Herschel discovered it again in
1795, and it was observed by several European astronomers. In 1805
it was again seen, and again in 1819. Hitherto it was supposed
that the four comets thus observed were all different; Encke,
however, showed that the observations could only be explained by
considering them as returns of the same revolving body; and by
doing this, well merited that his name should be associated with
the subject of his discovery. The return of this body in 1822,
was calculated beforehand, and observed in New South Wales, the
comet being then in the southern part of the heavens; but on
comparing the calculated and the observed places, Encke concluded
that the observations could not be exactly explained, without
supposing a resisting medium. This comet was again generally
observed in Europe in 1825 and 1828, and the circumstances of the
last appearance were particularly favourable for determining the
absolute amount of the retardation arising from the medium, which
the other observations had left undetermined.
The effect of this retarding influence is, as might be supposed
from what has already been said, extremely slight; and would
probably not have been perceptible at all, but for the loose
texture and small quantity of matter of the revolving body. It will
easily be conceived that a body which has perhaps no more solidity
or coherence than a cloud of dust, or a wreath of smoke, will have
less force to make its way through a fluid medium, however thin,
than a more dense and compact body would have. In atmospheric air
much rarefied, a bullet might proceed for miles without losing any
of its velocity, while such a loose mass as the comet is supposed
to be would lose its projectile motion in the space of a few
yards. This consideration will account for the circumstance, that
the existence of such a medium has been detected by observing the
motions of Encke’s comet, though the motions of the heavenly bodies
previously observed showed no trace of such an impediment.
It will appear perhaps remarkable that a body so light and loose as
we have described this comet to be, should revolve about the sun by
laws as fixed and certain as those which regulate the motions of
those great and solid masses, the Earth and Jupiter. It is however
certain from observation, that this comet is acted upon by exactly
the same force of solar attraction, as the other bodies of the
system; and not only so, but that it also experiences the same kind
of disturbing force from the action of the other planets, which
they exercise upon each other. The effect of all these causes has
been calculated with great care and labour; and the result has been
an agreement with observation sufficiently close to show that these
causes really act, but at the same time a _residual phenomenon_
(as Sir J. Herschel expresses it) has come to light: and from this
has been collected the inference of a resisting medium.
This medium produces a very small effect upon the motion of the
comet, as will easily be supposed from what has been said. By
Encke’s calculation, it appears that the effect of the resistance,
supposing the comet to move in the earth’s orbit, would be about
an eight hundred and fiftieth of the sun’s force on the body. The
effect of such resistance may appear, at first sight, paradoxical;
it would be to make the comet _move_ more slowly, but _perform
its revolutions_ more quickly. This, however, will perhaps be
understood if it be considered that by _moving_ more slowly the
comet will be more rapidly _drawn_ towards the centre, and that in
this way a revolution will be described by a shorter path than it
was before. It appears that in getting round the sun, the comet
gains more in this way than it loses by the diminution of its
velocity. The case is much like that of a stone thrown in the air;
the stone moves more slowly than it would do if there were no air;
but yet it comes to the earth _sooner_ than it would do on that
supposition.
It appears that the effect of the resistance of the ethereal
medium, from the first discovery of the comet up to the present
time, has been to diminish the time of revolution by about two
days: and the comet is ten days in advance of the place which it
would have reached, if there had been no resistance.
2. The same medium which is thus shown to produce an effect upon
Encke’s comet, must also act upon the planets which move through
the same spaces. The effect upon the planets, however, must be very
much smaller than the effect upon the comet, in consequence of
their greater quantity of matter.
It is not easy to assign any probable value, or even any certain
limit, to the effect of the resisting medium upon the planets.
We are entirely ignorant of the comparative mass of the comet,
and of any of the planets; and hence, cannot make any calculation
founded on such a comparison. Newton has endeavoured to show how
small the resistance of the medium must be, if it exist.[22] The
result of his calculation is, that if we take the density of the
medium to be that which our air will have at two hundred miles from
the earth’s surface, supposing the law of diminution of density
to go on unaltered, and if we suppose Jupiter to move in such a
medium, he would in a million years lose less than a millionth
part of his velocity. If a planet, revolving about the sun, were
to lose any portion of its velocity by the effect of resistance,
it would be drawn proportionally nearer the sun, the tendency
towards the centre being no longer sufficiently counteracted by
that centrifugal force which arises from the body’s velocity. And
if the resistance were to continue to act, the body would be drawn
perpetually nearer and nearer to the centre, and would describe its
revolutions quicker and quicker, till at last it would reach the
central body, and the system would cease to be a system.
This result is true, however small be the velocity lost by
resistance; the only difference being, that when the resistance
is small, the time requisite to extinguish the whole motion will
be proportionally longer. In all cases the times which come under
our consideration in problems of this kind, are enormous to common
apprehension. Thus Encke’s comet, according to the results of
the observations already made, will lose, in ten revolutions, or
thirty-three years, less than one thousandth of its velocity:
and if this law were to continue, the velocity would not be
reduced to one-half its present value in less than seven thousand
revolutions or twenty-three thousand years. If Jupiter were to
lose one-millionth of his velocity in a million years, (which,
as has been seen, is far more than can be considered in any way
probable,) he would require seventy millions of years to lose
one-thousandth of the velocity; and a period seven hundred times as
long to reduce the velocity to one-half. These are periods of time
which quite overwhelm the imagination; and it is not pretended that
the calculations are made with any pretensions to accuracy. But
at the same time it is beyond doubt that though the intervals of
time thus assigned to these changes are highly vague and uncertain,
the changes themselves must, sooner or later, take place, in
consequence of the existence of the resisting medium. Since there
is such a retarding force perpetually acting, however slight it
be, it must in the end destroy all the celestial motions. It may
be millions of millions of years before the earth’s retardation
may perceptibly affect the apparent motion of the sun; but still
the day will come (if the same Providence which formed the system,
should permit it to continue so long) when this cause will entirely
change the length of our year and the course of our seasons, and
finally stop the earth’s motion round the sun altogether. The
smallness of the resistance, however small we choose to suppose it,
does not allow us to escape this certainty. There is a resisting
medium; and, therefore, the movements of the solar system cannot go
on for ever. The moment such a fluid is ascertained to exist, the
eternity of the movements of the planets becomes as impossible as a
perpetual motion on the earth.
3. The vast periods which are brought under our consideration
in tracing the effects of the resisting medium, harmonize with
all that we learn of the constitution of the universe from
other sources. Millions, and millions of millions of years are
expressions that at first sight appear fitted only to overwhelm and
confound all our powers of thought; and such numbers are no doubt
beyond the limits of any thing which we distinctly conceive. But
our powers of conception are suited rather to the wants and uses
of common life, than to a complete survey of the universe. It is in
no way unlikely that the whole duration of the solar system should
be a period immeasurably great in our eyes, though demonstrably
finite. Such enormous numbers have been brought under our notice
by all the advances we have made in our knowledge of nature. The
smallness of the objects detected by the microscope and of their
parts;--the multitude of the stars which the best telescopes of
modern times have discovered in the sky;--the duration assigned
to the globe of the earth by geological investigation;--all these
results require for their probable expression, numbers, which so
far as we see, are on the same gigantic scale as the number of
years in which the solar system will become entirely deranged.
Such calculations depend in some degree on our relation to the
vast aggregate of the works of our Creator; and no person who is
accustomed to meditate on these subjects will be surprised that
the numbers which such an occasion requires should oppress our
comprehension. No one who has dwelt on the thought of a universal
Creator and Preserver, will be surprised to find the conviction
forced upon the mind by every new train of speculation, that viewed
in reference to Him, our space is a point, our time a moment, our
millions a handful, our permanence a quick decay.
Our knowledge of the vast periods, both geological and
astronomical, of which we have spoken, is most slight. It is in
fact little more than that such periods exist; that the surface of
the earth has, at wide intervals of time, undergone great changes
in the disposition of land and water, and in the forms of animal
life; and that the motions of the heavenly bodies round the sun
are affected, though with inconceivable slowness, by a force which
must end by deranging them altogether. It would therefore be rash
to endeavour to establish any analogy between the periods thus
disclosed; but we may observe that they _agree_ in this, that
they reduce all things to the general rule of _finite duration_.
As all the geological states of which we find evidence in the
present state of the earth, have had their termination, so also the
astronomical conditions under which the revolutions of the earth
itself proceed, involve the necessity of a future cessation of
these revolutions.
The contemplative person may well be struck by this universal law
of the creation. We are in the habit sometimes of contrasting the
transient destiny of man with the permanence of the forests, the
mountains, the ocean,--with the unwearied circuit of the sun. But
this contrast is a delusion of our own imagination; the difference
is after all but one of degree. The forest tree endures for its
centuries and then decays; the mountains crumble and change, and
perhaps subside in some convulsion of nature; the sea retires,
and the shore ceases to resound with the “everlasting” voice of
the ocean: such reflections have already crowded upon the mind of
the geologist; and it now appears that the courses of the heavens
themselves are not exempt from the universal law of decay; that not
only the rocks and the mountains, but the sun and the moon have
the sentence “to end” stamped upon their foreheads. They enjoy
no privilege beyond man except a longer respite. The ephemeron
perishes in an hour; man endures for his three score years and ten;
an empire, a nation, numbers its centuries, it may be its thousands
of years; the continents and islands which its dominion includes
have perhaps their date, as those which preceded them have had; and
the very revolutions of the sky by which centuries are numbered
will at last languish and stand still.
To dwell on the moral and religious reflections suggested by
this train of thought is not to our present purpose; but we may
observe that it introduces a _homogeneity_, so to speak, into
the government of the universe. Perpetual change, perpetual
progression, increase and diminution, appear to be the rules of
the material world, and to prevail without exception. The smaller
portions of matter which we have near us, and the larger, which
appear as luminaries at a vast distance, different as they are
in our mode of conceiving them, obey the same laws of motion;
and these laws produce the same results; in both cases motion is
perpetually destroyed, except it be repaired by some living power;
in both cases the relative rest of the parts of a material system
is the conclusion to which its motion tends.
4. It may perhaps appear to some, that this acknowledgment of
the tendency of the system to derangement through the action of
a resisting medium is inconsistent with the argument which we
have drawn in a previous chapter, from the provisions for its
stability. In reality, however, the two views are in perfect
agreement, so far as our purpose is concerned. The main point
which we had to urge, in the consideration of the stability of
the system, was, not that it is constructed to last for ever,
but that while it lasts, the deviations from its mean condition
are very small. It is this property which fits the world for
its uses. To maintain either the past or the future eternity of
the world, does not appear consistent with physical principles,
as it certainly does not fall in with the convictions of the
religious man, in whatever way obtained. We conceive that this
state of things has had a beginning; we conceive that it will have
an end. But in the mean time we find it fitted, by a number of
remarkable arrangements, to be the habitation of living creatures.
The conditions which secure the stability, and the smallness of
the perturbations of the system, are among these provisions. If
the eccentricity of the orbit of Venus, or of Jupiter, were much
greater than it is, not only might some of the planets, at the
close of ages, fall into the sun or fly off into infinite space,
but also, in the intermediate time, the earth’s orbit might become
much more eccentric; the course of the seasons and the average of
temperature might vary from what they now are, so as to injure
or destroy the whole organic creation. By certain original
arrangements these destructive oscillations are prevented. So long
as the bodies continue to revolve, their orbits will not be much
different from what they now are. And this result is not affected
by the action of the resisting medium. Such a medium cannot
increase the small eccentricities of the orbits. The range of the
periodical oscillations of heat and cold will not be extended by
the mechanical effect of the medium, nor would be, even if its
density were incomparably greater than it is. The resisting medium
therefore does not at all counteract that which is most important
in the provision for the permanency of the solar system. If the
stability of the system had not been secured by the adjustments
which we described in a former chapter, the course of the seasons
might have been disturbed to an injurious or even destructive
extent in the course of a few centuries, or even within the limits
of one generation; by the effect of the resisting medium, the order
of nature remains unchanged for a period, compared with which the
known duration of the human race is insignificant.
But, it may be objected, the effect of the medium must be
ultimately to affect, the duration of the earth’s revolution round
the sun, and thus to derange those adaptations which depend on the
length of the year. And, without question, if we permit ourselves
to look forward to that inconceivably distant period at which the
effect of the medium will become sensible, this must be allowed
to be true, as has been already stated. Millions, and probably
millions of millions, of years express inadequately the distance of
time at which this cause would produce a serious effect. That the
machine of the universe is so constructed that it may answer its
purposes for such a period, is surely sufficient proof of the skill
of its workmanship, and of the reality of its purpose: and those
persons, probably, who are best convinced that it is the work of
a wise and good Creator, will be least disposed to consider the
system as imperfect, because in its present condition it is not
fitted for eternity.
5. The doctrine of a Resisting Medium leads us towards a point
which the Nebular Hypothesis assumes;--a _beginning_ of the present
order of things. There must have been a commencement of the motions
now going on in the solar system. Since these motions, when once
begun, would be deranged and destroyed in a period which, however
large, is yet finite, it is obvious we cannot carry their origin
indefinitely backwards in a range of past duration. There is a
period in which these revolutions, whenever they had begun, would
have brought the revolving bodies into contact with the central
mass; and this period has in our system not yet elapsed. The watch
is still going, and therefore it must have been wound up within a
limited time.
The solar system, at this its beginning, must have been arranged
and put in motion by some cause. If we suppose this cause to
operate by means of the configurations and the properties of
previously existing matter, these configurations must have resulted
from some still previous cause, these properties must have produced
some previous effects. We are thus led to a condition still earlier
than the assumed beginning;--to an origin of the original state of
the universe; and in this manner we are carried perpetually further
and further back, through a labyrinth of mechanical causation,
without any possibility of finding any thing in which the mind
can acquiesce or rest, till we admit “a First Cause which is not
mechanical.”
Thus the argument which was before urged against those in
particular, who put forwards the Nebular Hypothesis in opposition
to the admission of an Intelligent Creator, offers itself again, as
cogent in itself, when we adopt the opinion of a resisting medium,
for which the physical proofs have been found to be so strong.
The argument is indeed forced upon our minds, whatever view we
take of the past history of the universe. Some have endeavoured
to evade its force by maintaining that the world as it now exists
has existed from eternity. They assert that the present order of
things, or an order of things in some way resembling the present,
produced by the same causes, governed by the same laws, has
prevailed through an infinite succession of past ages. We shall
not dwell upon any objections to this tenet which might be drawn
from our own conceptions, or from what may be called metaphysical
sources. Nor shall we refer to the various considerations which
history, geology, and astronomical records supply, and which tend
to show, not only that the past duration of the present course of
things is finite, but that it is short, compared with such periods
as we have had to speak of. But we may observe, that the doctrine
of a resisting medium once established, makes this imagination
untenable; compels us to go back to the origin, not only of the
present course of the world, not only of the earth, but of the
solar system itself; and thus sets us forth upon that path of
research into the series of past causation, where we obtain no
answer of which the meaning corresponds to our questions, till
we rest in the conclusion of a most provident and most powerful
Creating Intelligence.
It is related of Epicurus that when a boy, reading with his
preceptor these verses of Hesiod,
Ητοι μεν πρωτιζα Χαος γενετ’, αυταρ επειτα
Γαι’ ευρυζερνος παντων εδος ασφαλες αιει
Αθανατων,
Eldest of beings, Chaos first arose,
Thence Earth wide stretched, the steadfast seat of all
The Immortals,
the young scholar first betrayed his inquisitive genius by asking
“And chaos whence?” When in his riper years he had persuaded
himself that this question was sufficiently answered by saying that
chaos arose from the concourse of atoms, it is strange that the
same inquisitive spirit did not again suggest the question “and
atoms whence?” And it is clear that however often the question
“whence?” had been answered, it would still start up as at first.
Nor could it suffice as an answer to say, that earth, chaos, atoms,
were portions of a series of changes which went back to eternity.
The preceptor of Epicurus informed him, that to be satisfied on the
subject of his inquiry, he must have recourse to the philosophers.
If the young speculator had been told that chaos (if chaos indeed
preceded the present order) was produced by an Eternal Being, in
whom resided purpose and will, he would have received a suggestion
which, duly matured by subsequent contemplation, might have led
him to a philosophy far more satisfactory than the material scheme
can ever be, to one who looks, either abroad into the universe, or
within into his own bosom.
CHAPTER IX.
_Mechanical Laws._
In the preceding observations we have supposed the laws, by which
different kinds of matter act and are acted upon, to be already in
existence; and have endeavoured to point out evidences of design
and adaptation, displayed in the selection and arrangement of these
materials of the universe. These materials are, it has appeared,
supplied in such measures and disposed in such forms, that by means
of their properties and laws the business of the world goes on
harmoniously and beneficially. But a further question occurs: how
came matter to have such properties and laws? Are these also to
be considered as things of selection and institution? And if so,
can we trace the reasons why the laws were established in their
present form; why the properties which matter actually possesses
were established and bestowed and bestowed upon it? We have already
attempted, in a previous part of this work, to point out some of
the advantages which are secured by the existing laws of heat,
light and moisture. Can we, in the same manner, point out the
benefits which arise from the present constitution of those laws
of matter which are mainly concerned in the production of cosmical
phenomena?
It will readily be perceived that the discussion of this point
must necessarily require some effort of abstract thought. The laws
and properties of which we have here to speak, the laws of motion
and the universal properties of matter, are so closely interwoven
with our conceptions of the external world, that we have great
difficulty in conceiving them not to exist, or to exist other than
they are. When we press or lift a stone, we can hardly imagine that
it could, by possibility, do otherwise than resist our effort by
its hardness and by its heaviness, qualities so familiar to us:
when we throw it, it seems inevitable that its motion should depend
on the impulse we give, just as we find that it invariably does.
Nor is it easy to say how far it is really possible to suppose
the fundamental attributes of matter to be different from what
they are. If we, in our thoughts, attempt to divest matter of its
powers of resisting and moving, it ceases to be matter, according
to our conceptions, and we can no longer reason upon it with any
distinctness. And yet it is certain that we can conceive the laws
of hardness and weight and motion to be quite different from what
they are, and can point out some of the consequences which would
result from such difference. The properties of matter, even the
most fundamental and universal ones, do not obtain by any absolute
necessity, resembling that which belongs to the properties of
geometry. A line touching a circle is _necessarily_ perpendicular
to a line drawn to the centre through the point touched; for
it may be shown that the contrary involves a contradiction. But
there is no contradiction in supposing that a body’s motion should
naturally diminish, or that its weight should increase in removing
further from the earth’s centre.
Thus the properties of matter and the laws of motion are what we
find them, not by virtue of any internal necessity which we can
understand. The study of such laws and properties may therefore
disclose to us the character of that external agency by which
we conceive them to have been determined to be what they are;
and this must be the same agency by which all other parts of the
constitution of the universe were appointed and ordered.
But we can hardly expect, with regard to such subjects, that
we shall be able to obtain any complete or adequate view of
the reasons why these general laws are so selected, and so
established. These laws are the universal basis of all operations
which go on, at any moment, in every part of space, with regard
to every particle of matter, organic and inorganic. All other
laws and properties must have a reference to these, and must be
influenced by them; both such as men have already discovered, and
the far greater number which remain still unknown. The general
economy and mutual relations of all parts of the universe, must
be subordinate to the laws of motion and matter of which we
here speak. We can easily suppose that the various processes of
nature, and the dependencies of various creatures, are affected
in the most comprehensive manner by these laws;--are simplified
by _their_ simplicity, made consistent by _their_ universality;
rendered regular by _their_ symmetry. We can easily suppose that
in this way there may be the most profound and admirable reasons
for the existence of the present universal properties of matter,
which we cannot apprehend in consequence of the limited nature
of our knowledge, and of our faculties. For, compared with the
whole extent of the universe, the whole aggregate of things and
relations and connexions which exist in it, our knowledge is
most narrow and partial, most shallow and superficial. We cannot
suppose, therefore, that the reasons which we discover for the
present form of the laws of nature go nearly to the full extent, or
to the bottom of the reasons, which a more complete and profound
insight would enable us to perceive. To do justice to such reasons,
would require nothing less than a perfect acquaintance with the
whole constitution of every part of creation; a knowledge which man
has not, and, so far as we can conceive, never can have.
We are certain, therefore, that our views, with regard to this
part of our subject, must be imperfect and limited. Yet still man
has _some_ knowledge with regard to various portions of nature;
and with regard to those most general and comparatively simple
facts to which we now refer, his knowledge is more comprehensive,
and goes deeper than it does in any other province. We conceive,
therefore, that we shall not be engaged in any rash or presumptuous
attempt, if we endeavour to point out some of the advantages which
are secured by the present constitution of some of the general
mechanical laws of nature; and to suggest the persuasion of that
purpose and wise design, which the selection of such laws will thus
appear to imply.
CHAPTER X.
_The Law of Gravitation._
We shall proceed to make a few observations on the Law of Gravity,
in virtue of which the motions of planets about the sun, and of
satellites about their planets take place; and by which also are
produced the fall downwards of all bodies within our reach, and
the pressure which they exert upon their supports when at rest.
The identification of the latter forces with the former, and the
discovery of the single law by which these forces are every where
regulated, was the great discovery of Newton: and we wish to make
it appear that this law is established by an intelligent and
comprehensive selection.
The law of the sun’s attraction upon the planets is, that this
attraction varies _inversely_ as the square of the distance; that
is, it decreases as that square increases. If we take three points
or planets of the solar system, the distances of which from the
sun are in proper proportion one, two, three; the attractive force
which the sun at these distances exercises, is as one, one-fourth,
and one-ninth respectively. In the smaller variations of distance
which occur in the elliptical motion of one planet, the variations
of the force follow the same law. Moreover, not only does the
sun attract the planets, but they attract each other according
to the same law; the tendency to the earth which makes bodies
heavy, is one of the effects of this law: and all these effects of
the attractions of large masses may be traced to the attractions
of the particles of which they are composed; so that the final
generalization, including all the derivative laws, is, that every
particle of matter in the universe attracts every other, according
to the law of the inverse square of the distance.
Such is the law of universal gravitation. Now, the question
is, why do either the attractions of masses, or those of their
component particles, follow this law of the inverse square of the
distance rather than any other? When the distance becomes one,
two, and three, why should not the force also become one, two, and
three?--or if it must be weaker at points more remote from the
attracting body, why should it not be one, a half, a third? or one,
an eighth, a twenty-seventh? Such law’s could easily be expressed
mathematically, and their consequences calculated. Can any reason
be assigned why the law which we find in operation _must_ obtain?
Can any be assigned why it _should_ obtain?
The answer to this is, that no reason, at all satisfactory, can be
given why such a law must, of necessity, be what it is; but that
very strong reasons can be pointed out why, for the beauty and
advantage of the system, the present one is better than others. We
will point out some of these reasons.
1. In the first place, the system could not have subsisted, if
the force had followed a _direct_ instead of an inverse law, with
respect to the distance; that is, if it had increased when the
distance increased. It has been sometimes said, that “all direct
laws of force are excluded on account of the danger from perturbing
forces;”[23] that if the planets had pulled at this earth, the
harder the further off they were, they would have dragged it
entirely out of its course. This is not an exact statement of
what would happen: if the force were to be simply in the direct
ratio of the distance, any number of planets might revolve in the
most regular and orderly manner. Their mutual effects, which we
may call perturbations if we please, would be considerable; but
these perturbations would be so combined with the unperturbed
motion, as to produce a new motion not less regular than the
other. This curious result would follow, that every body in the
system would describe, or seem to describe, about every other,
an exact elliptical orbit; and that the times of the revolution
of every body in its orbit would be all equal. This is proved by
Newton, in the sixty-fourth proposition of the Principia. There
would be nothing to prevent all the planets, on this supposition,
from moving round the sun in orbits exactly circular, or nearly
circular, according to the mode in which they were set in motion.
But though the perturbations of the system would not make this
law inadmissible, there are other circumstances which would do so.
Under this law, the gravity of bodies at the earth’s surface would
cease to exist. Nothing would fall or weigh downwards. The greater
action of the distant sun and planets would exactly neutralize the
gravity of the earth: a ball thrown from the hand, however gently,
would immediately become a satellite of the earth, and would for
the future accompany it in its course, revolving about it in the
space of one year. All terrestrial things would float about with no
principle of coherence or stability: they would obey the general
law of the system, but would acknowledge no particular relation
to the earth. We can hardly pretend to judge of the abstract
possibility of such a system of things; but it is clear that it
could not exist without an utter subversion of all that we can
conceive of the economy and structure of the world which we inhabit.
With any other direct law of force, we should in like manner
lose gravity, without gaining the theoretical regularity of
the planetary motions which we have described in the case just
considered.
2. Among _inverse_ laws of the distance, (that is, those according
to which the force diminishes as the distance from the origin of
force increases,) all which diminish the central force faster than
the _cube_ of the distance increases are inadmissible, because they
are incompatible with the permanent revolution of a planet. Under
such laws it would follow, that a planet would describe a spiral
line about the sun, and would either approach nearer and nearer to
him perpetually, or perpetually go further and further off: nearly
as a stone at the end of a string, when the string is whirled
round, and is allowed to wrap round the hand, or to unwrap from it,
approaches to or recedes from the hand.
If we endeavour to compare the law of the inverse square of
the distance, which really regulates the central force, with
other laws, not obviously inadmissible, as for instance, the
inverse simple ratio of the distance, a considerable quantity
of calculation is found to be necessary in order to trace the
results, and especially the perturbations in the two cases. The
perturbations in the supposed case have not been calculated;
such a calculation being a process so long and laborious that it
is never gone through, except for the purpose of comparing the
results of theory with those of observation, as we can do with
regard to the law of inverse square. We can only say, therefore,
that the stability of the system, and the moderate limits of the
perturbations, which we know to be secured by the existing law,
would not, so far as we know, be obtained by any different law.
Without going into further examination of the subject, we may
observe that there are some circumstances in which the present
system has a manifest superiority in its simplicity over the
condition which would have belonged to it if the force had followed
any other law. Thus, with the present law of gravitation the
planets revolve, returning perpetually on the same track, very
nearly. The earth describes an oval, in consequence of which motion
she is nearer to the sun in our winter than in our summer by about
one-thirtieth part of the whole distance. And, as the matter now
is, the nearest approach to the sun, and the farthest recess
from him, occur always at the same points of the orbit. There is
indeed a slight alteration in these points arising from disturbing
forces, but this is hardly sensible in the course of several ages.
Now if the force had followed any other law, we should have had
the earth running perpetually on a new track. The greatest and
least distances would have occurred at different parts in every
successive revolution. The orbit would have perpetually intersected
and been interlaced with the path described in former revolutions;
and the simplicity and regularity which characterizes the present
motion would have been quite wanting.
3. Another peculiar point of simplicity in the present law of
mutual attraction is this: that it makes the law of attraction for
spherical masses the same as for single particles. If particles
attract with forces which are inversely as the square of the
distance, spheres composed of such particles, will exert a force
which follows the same law. In this character the present law
is singular, among all possible laws, excepting that of the
direct distance which we have already discussed. If the law of
the gravitation of particles had been that of the inverse simple
distance, the attraction of a sphere would have been expressed by
a complex series of mathematical expressions, each representing
a simple law. It is truly remarkable that the law of the inverse
square of the distance, which appears to be selected as that of
the _masses_ of the system, and of which the mechanism is, that it
arises from the action of the _particles_ of the system, should
lead us to the same law for the action of these particles: there is
a striking _prerogative_ of simplicity in the law thus adopted.
The law of gravitation actually prevailing in the solar system has
thus great and clear advantages over any law widely different from
it; and has moreover, in many of its consequences, a simplicity
which belongs to this precise law alone. It is in many such
respects a _unique_ law; and when we consider that it possesses
several _properties_ which are _peculiar_ to it, and several
_advantages_ which may be peculiar to it, and which are certainly
nearly so; we have some ground, it would appear, to look upon its
peculiarities and its advantages as connected. For the reasons
mentioned in the last chapter, we can hardly expect to see fully
the way in which the system is benefited by the simplicity of this
law, and by the mathematical elegance of its consequences: but when
we see that it has some such beauties, and some manifest benefits,
we may easily suppose that our ignorance and limited capacity alone
prevent our seeing that there are, for the selection of this law of
force, reasons of a far more refined and comprehensive kind than
we can distinctly apprehend.
4. But before quitting this subject we may offer a few further
observations on the question, whether gravitation and the law of
gravitation be _necessary_ attributes of matter. We have spoken of
the selection of this law, but is it selected? Could it have been
otherwise? Is not the force of attraction a necessary consequence
of the fundamental properties of matter?
This is a question which has been much agitated among the followers
of Newton. Some have maintained, as Cotes, that gravity is an
inherent property of all matter; others, with Newton himself, have
considered it as an appendage to the essential qualities of matter,
and have proposed hypotheses to account for the mode in which its
effects are produced.
The result of all that can be said on the subject appears to be
this: that no one can demonstrate the possibility of deducing
gravity from the acknowledged fundamental properties of matter: and
that no philosopher asserts, that matter has been found to exist,
which was destitute of gravity. It is a property which we have no
right to call _necessary_ to matter, but every reason to suppose
_universal_.