seem the more necessary to be premised, because the general phraseology
of physical science, taken as language is commonly received, will seem
to convey something more. The names of the several attractions which
we shall have to notice, frequently refer the seat of the cause to
specific objects, and seem to imply something respecting its mode of
operation. Thus, when we say “the magnet attracts a piece of iron,” the
true philosophical import of the words is, “that a piece of iron placed
in the vicinity of the magnet, will move towards it, or placed in
contact, will adhere to it, so that some force is necessary to separate
them.” In the ordinary sense, however, something more than this simple
fact is implied. It is insinuated that the magnet is the seat of the
force which gives motion to the iron; that in the production of the
phenomenon, the magnet is an _agent_ exerting a certain influence, of
which the iron is the _subject_. Of all this, however, there is no
proof; on the contrary, since the magnet must move towards the iron
with just as much force as the iron moves towards the magnet, there is
as much reason to place the seat of the force in the iron, and consider
it as an agent affecting the magnet. But, in fact, the influence
which produces this phenomenon may not be resident in either the one
body or the other. It may be imagined to be a property of a medium in
which both are placed, or to arise from some third body, the presence
of which is not immediately observed. However attractive these and
like speculations may be, they cannot be allowed a place in physical
investigations, nor should consequences drawn from such hypotheses be
allowed to taint our conclusions with their uncertainty.
The student ought, therefore, to be aware, that whatever may seem
to be implied by the language used in this science in relation to
attractions, nothing is permitted to form the basis of reasoning
respecting them except _their effects_; and whatever be the common
signification of the terms used, it is to these effects, and to these
alone, they should be referred.
(97.) Attractions may be primarily distributed into two classes; one
consisting of those which exist between the molecules or constituent
parts of bodies, and the other between bodies themselves. The former
are sometimes called, for distinction, _molecular_ or _atomic_
attractions.
Without the agency of molecular forces, the whole face of nature would
be deprived of variety and beauty; the universe would be a confused
heap of material atoms dispersed through space, without form, shape,
coherence, or motion. Bodies would neither have the forms of solid,
liquid, or air; heat and light would no longer produce their wonted
effects; organised beings could not exist; life itself, as connected
with body, would be extinct. Atoms of matter, whether distant or in
juxtaposition, would have no tendency to change their places, and all
would be eternal stillness and rest. If, then, we are asked for a proof
of the existence of molecular forces, we may point to the earth and
to the heavens; we may name every object which can be seen or felt.
The whole material world is one great result of the influence of these
powerful agents.
(98.) It has been proved (11. _et seq._) that the constituent particles
of bodies are of inconceivable minuteness, and that they are not in
immediate contact (23), but separated from each other by interstitial
spaces, which, like the atoms themselves, although too small to be
directly observed, yet are incontestably proved to exist, by observable
phenomena, from which their existence demonstratively follows. The
resistance which every body opposes to compression, proves that a
repulsive influence prevails between the particles, and that this
repulsion is the cause which keeps the atoms separate, and maintains
the interstitial spaces just mentioned. Although this repulsion is
found to exist between the molecules of all substances whatever, yet
it has different degrees of energy in different bodies. This is proved
by the fact, that some substances admit of easy compression, while in
others, the exertion of considerable force is necessary to produce the
smallest diminution in bulk.
The space around each atom of a body, through which this repulsive
influence extends, is generally limited, and immediately beyond it, a
force of the opposite kind is manifested, viz. attraction. Thus, in
solid bodies, the particles resist separation as well as compression,
and the application of force is as necessary to break the body, or
divide it into separate parts, as to force its particles into closer
aggregation. It is by virtue of this attraction that solid bodies
maintain their figure, and that their parts are not separated and
scattered like those of fluids, merely by their own weight. This force
is called the _attraction of cohesion_.
The cohesive force acts in different substances with different degrees
of energy: in some its intensity is very great; but the sphere of its
influence apparently very limited. This is the case with all bodies
which are hard, strong, and brittle, which no force can extend or
stretch in any perceptible degree, and which require a great force to
break or tear them asunder. Such, for example, is cast iron, certain
stones, and various other substances. In some bodies the cohesive force
is weak, but the sphere of its action considerable. Bodies which are
easily extended, without being broken or torn asunder, furnish examples
of this. Such are Indian-rubber, or caoutchouc, several animal and
vegetable products, and, in general, all solids of a soft and viscid
kind.
Between these extremes, the cohesive force may be observed in various
degrees. In lead and other soft metals, its sphere of action is
greater, and its energy less, than in the former examples; but its
sphere less, and energy greater, than in the latter ones. It is from
the influence of this force, and that of the repulsion, whose sphere of
action is still closer to the component atoms, that all the varieties
of texture which we denominate hard, soft, tough, brittle, ductile,
pliant, &c. arise.
After having been broken, or otherwise separated, the parts of a solid
may be again united by their cohesion, provided any considerable
number of points be brought into sufficiently close contact. When this
is done by mechanical means, however, the cohesion is not so strong
as before their separation, and a comparatively small force will be
sufficient again to disunite them. Two pieces of lead freshly cut, with
smooth surfaces, will adhere when pressed together, and will require a
considerable force to separate them. In the same manner if a piece of
Indian-rubber be torn, the parts separated will again cohere, by being
brought together with a slight pressure. The union of the parts in
such instances is easy, because the sphere through which the influence
of cohesion extends is considerable; but even in bodies in which
this influence extends through a more limited space, the cohesion of
separate pieces will be manifested, provided their surfaces be highly
polished, so as to insure the near approach of a great number of their
particles. Thus, two polished surfaces of glass, metal, or stone, will
adhere when brought into contact.
In all these cases, if the bodies be disunited by mechanical force,
they will separate at exactly the parts at which they had been united,
so that after their separation no part of the one will adhere to the
other; proving that the force of cohesion of the surfaces brought into
contact is less than that which naturally held the particles of each
together.
(99.) When a body is in the liquid form, the weight of its particles
greatly predominates over their mutual cohesion, and consequently if
such a body be unconfined it will be scattered by its own weight; if
it be placed in any vessel, it will settle itself, by the force of its
weight, into the lowest parts, so that no space in the vessel below
the upper surface of the liquid will be unoccupied. The particles of
a solid body placed in the vessel have exactly the same tendency, by
reason of their weight; but this tendency is resisted and prevented
from taking effect by their strong cohesion.
Although this cohesion in solids is much greater than in liquids, and
productive of more obvious effects, yet the principle is not altogether
unobserved in liquids. Water converted into vapour by heat, is divided
into inconceivably minute particles, which ascend in the atmosphere.
When it is there deprived of a part of that heat which gave it the
vaporous form, the particles, in virtue of their cohesive force,
collect into round drops, in which form they descend to the earth.
In the same manner, if a liquid be allowed to fall gradually from the
lip of a vessel, it will not be dismissed in particles indefinitely
small, as if its mass were incoherent, like sand or powder, but will
fall in drops of considerable magnitude. In proportion as the cohesive
force is greater, these drops affect a greater size. Thus, oil and
viscid liquids fall in large drops; ether, alcohol, and others in small
ones.
Two drops of rain trickling down a window pane will coalesce when they
approach each other; and the same phenomenon is still more remarkable,
if a few drops of quicksilver be scattered on an horizontal plate of
glass.
It is the cohesive principle which gives rotundity to grains of shot:
the liquid metal is allowed to fall like rain from a great elevation.
In its descent the drops become truly globular, and before they reach
the end of their fall they are hardened by cooling, so that they retain
their shape.
It is also, probably, to the cohesive attraction that we should assign
the globular forms of all the great bodies of the universe; the sun,
planets, satellites, &c., which originally may have been in the liquid
state.
(100.) Molecular attraction is also exhibited between the particles of
liquids and solids. A drop of water will not descend freely when it
is in contact with a perpendicular glass plane: it will adhere to the
glass; its descent will be retarded; and if its weight be insufficient
to overcome the adhesive force, it will remain suspended.
If a plate of glass be placed upon the surface of water without being
permitted to sink, it will require more force to raise it from the
water than is sufficient merely to balance the weight of the glass.
This shows the adhesion of the water and glass, and also the cohesive
force with which the particles of the water resist separation.
If a needle be dipped in certain liquids, a drop will remain suspended
at its point when withdrawn from them: and, in general, when a solid
body has been immersed in a liquid and withdrawn, it is _wet_; that
is, some of the liquid has adhered to its surfaces. If no attraction
existed between the solid and liquid, the solid would be in the same
state after immersion as before. This is proved by liquids and solids
between which no attraction exists. If a piece of glass be immersed in
mercury, it will be in the same state when withdrawn as before it was
immersed. No mercury will adhere to it; it will not be _wet_.
When it rains, the person and vesture are affected only because this
attraction exists between them and water. If it rained mercury, none
would adhere to them.
(101.) When molecular attraction is exhibited by liquids pervading the
interstices of porous bodies, ascending in crevices or in the bores of
small tubes, it is called _capillary attraction_. Instances of this
are innumerable. Liquids are thus drawn into the pores of sponge,
sugar, lamp-wick, &c. The animal and vegetable kingdom furnish numerous
examples of this class of effects.
A weight being suspended by a dry rope, will be drawn upwards through
a considerable height, if the rope be moistened with a wet sponge. The
attraction of the particles composing the rope for the water is in this
case so powerful, that the tension produced by several hundred weight
cannot expel them.
A glass tube, of small bore, being dipped in water tinged by mixture
with a little ink, will retain a quantity of the liquid suspended when
withdrawn. The height of the liquid in the tube will be seen by looking
through it. It is found that the less the bore of the tube is, the
greater will be the height of the column sustained. A series of such
tubes fixed in the same frame, with their lower orifices at the same
level, and with bores gradually decreasing, being dipped in the liquid,
will exhibit columns gradually increasing.
A _capillary syphon_ is formed of a hank of cotton threads, one end of
which is immersed in the vessel containing the liquid, and the other is
carried into the vessel into which the liquid is to be transferred. The
liquid may be thus drawn from the one vessel into the other. The same
effect may be produced by a glass syphon with a small bore.
(102.) It frequently happens that a _molecular repulsion_ is exhibited
between a solid and a liquid. If a piece of wood be immersed in
quicksilver, the liquid will be depressed at that part of the surface
which is near the wood; and in like manner, if it be contained in a
glass vessel, it will be depressed at the edges. In a barometer tube,
the surface of the mercury is convex, owing partly to the repulsion
between the glass and mercury.
All solids, however, do not repel mercury. If any golden trinket be
dipped in that liquid, or even be exposed for a moment to contact
with it, the gold will be instantly intermingled with particles of
quicksilver, the metal changes its colour, and becomes white like
silver, and the mercury can only be extricated by a difficult process.
Chains, seals, rings, &c. should always be laid aside by those engaged
in experiments or other processes in which mercury is used.
(103.) Of all the forms under which molecular force is exhibited,
that in which it takes the name of _affinity_ is attended with the
most conspicuous effects. Affinity is in chemistry what inertia is
in mechanics, the basis of the science. The present treatise is not
the proper place for any detailed account of this important class
of natural phenomena. Those who seek such knowledge are referred
to our treatise on CHEMISTRY. Since, however, affinity sometimes
influences the mechanical state of bodies, and affects their mechanical
properties, it will be necessary here to state so much respecting it as
to render intelligible those references which we may have occasion to
make to such effects.
When the particles of different bodies are brought into close contact,
and more especially when, being in a fluid state, they are mixed
together, their union is frequently observed to produce a compound
body, differing in its qualities from either of the component bodies.
Thus the bulk of the compound is often greater or less than the united
volumes of the component bodies. The component bodies may be of the
ordinary temperature of the atmosphere, and yet the compound may be of
a much higher or lower temperature. The components may be liquid, and
the compound solid. The colour of the compound may bear no resemblance
whatever to that of the components. The species of molecular action
between the components, which produce these and similar, effects, is
called _affinity_.
(104.) We shall limit ourselves here to the statement of a few examples
of these phenomena.
If a pint of water and a pint of sulphuric acid be mixed, the compound
will be considerably less than a quart. The density of the mixture is,
therefore, greater than that which would result from the mere diffusion
of the particles of the one fluid through those of the other. The
particles have assumed a greater proximity, and therefore exhibit a
mutual attraction.
In this experiment, although the liquids before being mixed be of the
temperature of the surrounding air, the mixture will be so intensely
hot, that the vessel which contains it cannot be touched without pain.
If the two aeriform fluids, called oxygen and hydrogen, be mixed
together in a certain proportion, the compound will be water. In this
case, the components are different from the compound, not merely in
the one being _air_ and the other _liquid_, but in other respects
not less striking. The compound water extinguishes fire, and yet of
the components, hydrogen is one of the most inflammable substances
in nature, and the presence of oxygen is indispensably necessary to
sustain the phenomenon of combustion.
Oxygen gas, united with quicksilver, produces a compound of a black
colour, the quicksilver being white and the gas colourless. When
these substances are combined in another proportion, they give a red
compound.
(105.) Having noticed the principal molecular forces, we shall now
proceed to the consideration of those attractions which are exhibited
between bodies existing in masses. The influence of molecular
attractions is limited to insensible distances. On the contrary, the
forces which are now to be noticed act at considerable distances,
and to the influence of some there is no limit, the effect, however,
decreasing as the distance increases.
The effect of the loadstone on iron is well known, and is one of this
class of forces. For a detailed account of this force, and the various
phenomena of which it is the cause, the reader is referred to our
treatise on MAGNETISM.
When glass, wax, amber, and other substances are submitted to friction
with silken or woollen cloth, they are observed to attract feathers,
and other light bodies placed near them. A like effect is produced
in several other ways, and is attended with other phenomena, the
discussion of which forms a principal part of physical science. The
force thus exhibited is called electricity. For details respecting it,
and for its connection with magnetism, the reader is referred to our
treatises on ELECTRICITY and ELECTRO-MAGNETISM.
(106.) These attractions exist either between bodies of particular
kinds, or are developed by reducing the bodies which manifest them to
a certain state by friction, or some other means. There is, however,
an attraction, which is manifested between bodies of all species, and
under all circumstances whatever; an attraction, the intensity of which
is wholly independent of the nature of the bodies, and only depends on
their masses and mutual distances. Thus, if a mass of metal and a mass
of clay be placed in the vast abyss of space, at a mile asunder, they
will instantly commence to approach each other with certain velocities.
Again, if a mass of stone and of wood respectively equal to the former,
be placed at a like distance, they will also commence to approach
each other with the same velocities as the former. This universal
attraction, which only depends on the quantity of the masses and their
mutual distances, is called the “attraction of gravitation.” We shall
first explain the “law” of this attraction, and shall then point out
some of the principal phenomena by which its existence and its laws are
known.
(107.) The “law of gravitation” sometimes from its universality called
the “law of nature,” may be explained as follows:
Let us suppose two masses, A and B, placed beyond the influence or
attraction of any other bodies, in a state of rest, and at any proposed
distance from each other. By their mutual attraction they will approach
each other, but not with the same velocity. The velocity of A will be
greater than that of B, in the same proportion as its mass is less
than that of B. Thus, if the mass of B be twice that of A, while A
approaches B through a space of two feet, B will approach A through a
space of one foot. Hence it follows, that the force with which A moves
towards B is equal to the force with which B moves towards A (68). This
is only a consequence of the property of inertia, and is an example of
the equality of action and reaction, as explained in Chapter IV. The
velocity with which A and B approach each other is estimated by the
diminution of their distance, A B, by their mutual approach in a
given time. Thus, if in one second A move towards B through a space of
two feet, and in the same time B moves towards A through the space of
one foot, they will approach each other through a space of three feet
in a second, which will be their relative velocity (91).
If the mass of B be doubled, it will attract A with double the former
force, or, what is the same, will cause A to approach B with double the
former velocity. If the mass of B be trebled, it will attract A with
treble the first force, and, in general, while the distance A B
remains the same, the attractive force of B upon A will increase or
diminish in exactly the same proportion as the mass of B is increased
or diminished.
In the same manner, if the mass A be doubled, it will be attracted by
B with a double force, because B exerts the same degree of attraction
on every part of the mass A, and any addition which it may receive will
not diminish or otherwise affect the influence of B on its former mass.
To express this in general arithmetical symbols let _a_ and _b_ express
the space through which A and B respectively would be moved towards
each other by their mutual attraction. We would then have
A × _a_ = B × _b_.
Thus, it is a general law of gravitation, that so long as the distance
between two bodies remains the same, each will attract and be attracted
by the other, in proportion to its mass; and any increase or decrease
of the mass will cause a corresponding increase or decrease in the
amount of the attraction.
(108.) We shall now explain the law, according to which the attraction
is changed, by changing the distance between the bodies. At the
distance of one mile the body B attracts A with a certain force. At the
distance of two miles, the masses not being changed, the attraction of
B upon A will be one-fourth of its amount at the distance of one mile.
At the distance of three miles, it will be one-ninth of its original
amount; at four miles, it is reduced to a sixteenth, and so on. The
following table exhibits the diminution of the attraction corresponding
to the successive increase of distance:
+-----------+---+----+----+----+----+----+----+----+----+
|Distance | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | &c.|
+-----------+---+----+----+----+----+----+----+----+----+
|Attraction | 1 | 1/4| 1/9|1/16|1/25|1/36|1/49|1/64| &c.|
+-----------+---+----+----+----+----+----+----+----+----+
In ARITHMETIC, that number which is found by multiplying any proposed
number by itself, is called its _square_. Thus 4, that is, 2 multiplied
by 2, is the square of 2; 9 that is, 3 times 3, is the square of 3, and
so on. On inspecting the above table, it will be apparent, therefore,
that the attraction of gravitation decreases in the same proportion as
the square of the distance from the attracting body increases, the mass
of both bodies in this case being supposed to remain the same; but if
the mass of either be increased or diminished, the attraction will be
increased or diminished in the same proportion.
(109.) Hence the _law of gravitation_ may be thus expressed: “The
mutual attraction of two bodies increases in the same proportion
as their masses are increased, and as the square of their distance
is decreased; and it decreases in proportion as their masses are
decreased, and as the square of their distance is increased.”
This law may be more clearly expressed by means of general symbols.
Let _f_ express the force with which a mass weighing 1 lb. will
attract another mass weighing 1 lb., at the distance of 1 foot.
The force with which they will mutually attract, when removed to the
distance expressed in feet by D, will be
_f_/D^2
that is, the force _f_ divided by the square of the number D.
If one of the bodies, instead of weighing 1 lb., weigh the number
of pounds expressed by A, their mutual attraction will be increased A
times, and will therefore be expressed by
(A × _f_)/D^2
In fine, if the other be also the number of pounds expressed by B,
their mutual attraction will be
(A × B × _f_)/D^2
(110.) Having explained the law of gravitation, we shall now proceed to
show how the existence of this force is proved, and its law discovered.