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A
TREATISE ON MECHANICS,
BY
CAPTAIN HENRY KATER, V. PRES: R.S.
----and----
DIONYSIUS LARDNER, D.C.L. F.R.S. &c. &c.
A NEW EDITION REVISED & CORRECTED.
1852.
[Illustration: _H. Corbould del._ _E. Finder fc._]
London:
PRINTED FOR LONGMAN, BROWN, GREEN & LONGMANS. PATERNOSTER ROW:
ADVERTISEMENT.
This Treatise on Mechanics, which was originally published in 1830,
is the work of Dr. Lardner, with the exception of the twenty-first
chapter, which was written by the late Captain Kater. The present
edition has been revised and corrected by Dr. Lardner.
_London, January, 1852._
CONTENTS.
CHAP. I.
PROPERTIES OF MATTER.
Organs of Sense.--Sensations.--Properties or Qualities.--Observation.
--Comparison and Generalisation.--Particular and general Qualities.--
Magnitude.--Size.--Volume.--Lines.--Surfaces.--Edges.--Area.--Length.
--Impenetrability.--Apparent Penetration.--Figure.--Different from
Volume.--Atoms.--Molecules.--Matter separable.--Particles.--Force.--
Cohesion of Atoms.--Hypothetical Phrases unnecessary.--Attraction. 1
CHAP. II.
PROPERTIES OF MATTER, CONTINUED.
Divisibility.--Unlimited Divisibility.--Wollaston’s micrometric
Wire. --Method of making it.--Thickness of a Soap Bubble.--Wings of
Insects. --Gilding of Wire for Embroidery.--Globules of the Blood.--
Animalcules.--Their minute Organisation.--Ultimate Atoms.--Crystals.--
Porosity.--Volume.--Density.--Quicksilver passing through Pores of
Wood.--Filtration.--Porosity of Hydrophane.--Compressibility.--
Elasticity.--Dilatability.--Heat.--Contraction of Metal used to
restore the Perpendicular to Walls of a Building.--Impenetrability of
Air.--Compressibility of it.--Elasticity of it.--Liquids not absolutely
incompressible.--Experiments.--Elasticity of Fluids.-- Aeriform
Fluids.--Domestic Fire Box.--Evolution of Heat by compressed Air. 9
CHAP. III.
INERTIA.
Inertia.--Matter Incapable of spontaneous Change.--Impediments to
Motion.--Motion of the Solar System.--Law of Nature.--Language used
to express Inertia sometimes faulty.--Familiar Examples of Inertia. 27
CHAP. IV.
ACTION AND REACTION.
Inertia in a single Body.--Consequences of Inertia in two or more
Bodies.--Examples.--Effects of Impact.--Motion not estimated by
Speed or Velocity alone.--Examples.--Rule for estimating the
Quantity of Motion.--Action and Reaction.--Examples of.--Velocity
of two Bodies after Impact.--Rule for finding the common Velocity
after Impact.--Magnet and Iron.--Feather and Cannon Ball impinging.
--Newton’s Laws of Motion.--Inutility of.--Familiar Effects
resulting from Consequences of Inertia. 34
CHAP. V.
COMPOSITION AND RESOLUTION OF FORCE.
Motion and Pressure.--Force.--Attraction.--Parallelogram of Forces.
--Resultant.--Components.--Composition of Force.--Resolution of
Force.--Illustrative Experiments.--Composition of Pressures.--
Theorems regulating Pressures also regulate Motion.--Examples.--
Resolution of Motion.--Forces in Equilibrium.--Composition of Motion
and Pressure.--Illustrations.--Boat in a Current.--Motions of Fishes.
--Flight of Birds.--Sails of a Vessel.--Tacking.--Equestrian Feats.
--Absolute and relative Motion. 48
CHAP. VI.
ATTRACTION.
Impulse.--Mechanical State of Bodies.--Absolute Rest.--Uniform and
rectilinear Motion.--Attractions.--Molecular or atomic.--Interstitial
Spaces in Bodies.--Repulsion and Attraction.--Cohesion.--In Solids
and Fluids.--Manufacture of Shot.--Capillary Attractions.--Shortening
of Rope by Moisture.--Suspension of Liquids in capillary Tubes.--
Capillary Siphon.--Affinity between Quicksilver and Gold.--Examples
of Affinity.--Sulphuric Acid and Water.--Oxygen and Hydrogen.--Oxygen
and Quicksilver.--Magnetism.--Electricity and Electro-Magnetism.--
Gravitation.--Its Law.--Examples of.--Depends on the Mass.--
Attraction between the Earth and detached Bodies on its Surface.--
Weight.--Gravitation of the Earth.--Illustrated by Projectiles.--
Plumb-Line.--Cavendish’s Experiments. 63
CHAP. VII.
TERRESTRIAL GRAVITY.
Phenomena of falling Bodies.--Gravity greater at the Poles than
Equator.--Heavy and light Bodies fall with equal Speed to the Earth.
--Experiment.--Increased Velocity of falling Bodies.--Principles of
uniformly accelerated Motion.--Relations between the Height, Time,
and Velocity.--Attwood’s Machine.--Retarded Motion. 84
CHAP. VIII.
OF THE MOTION OF BODIES ON INCLINED PLANES AND CURVES.
Force perpendicular to a Plane.--Oblique Force.--Inclined Plane.--
Weight produces Pressure and Motion.--Motion uniformly accelerated.--
Space moved through in a given Time.--Increased Elevation produces
increased Force.--Perpendicular and horizontal Plane.--Final
Velocity.--Motion down a Curve.--Depends upon Velocity and Curvature.
--Centrifugal Force.--Circle of Curvature.--Radius of Curvature.--
Whirling Table.--Experiments.--Solar System.--Examples of centrifugal
Force. 85
CHAP. IX.
THE CENTRE OF GRAVITY.
Terrestrial Attraction the combined Action of parallel Forces.--
Single equivalent Force.--Examples.--Method of finding the Centre of
Gravity.--Line of Direction.--Globe.--Oblate Spheroid.--Prolate
Spheroid.--Cube.--Straight Wand.--Flat Plate.--Triangular Plate.--
Centre of Gravity not always within the Body.--A Ring.--Experiments.
--Stable, instable, and neutral Equilibrium.--Motion and Position of
the Arms and Feet.--Effect of the Knee-Joint.--Positions of a Dancer.
--Porter under a Load.--Motion of a Quadruped.--Rope Dancing.--
Centre of Gravity of two Bodies separated from each other.--
Mathematical and experimental Examples.--The Conservation of the
Motion of the Centre of Gravity.--Solar System.--Centre of Gravity
sometimes called Centre of Inertia. 107
CHAP. X.
THE MECHANICAL PROPERTIES OF AN AXIS.
An Axis.--Planets and common spinning Top.--Oscillation or Vibration.
--Instantaneous and continued Forces.--Percussion.--Continued Force.
--Rotation.--Impressed Forces.--Properties of a fixed Axis.--Movement
of the Force round the Axis.--Leverage of the Force.--Impulse
perpendicular to, but not crossing, the Axis.--Radius of Gyration.--
Centre of Gyration.--Moment of Inertia.--Principal Axes.--Centre of
Percussion. 128
CHAP. XI.
OF THE PENDULUM.
Isochronism.--Experiments.--Simple Pendulum.--Examples illustrative
of.--Length of.--Experiments of Kater, Biot, Sabine, and others.--
Huygens’ Cycloidal Pendulum. 145
CHAP. XII.
OF SIMPLE MACHINES.
Statics.--Dynamics.--Force.--Power.--Weight.--Lever.--Cord.--
Inclined Plane. 160
CHAP. XIII.
OF THE LEVER.
Arms.--Fulcrum.--Three Kinds of Levers.--Crow Bar.--Handspike.--Oar.
--Nutcrackers.--Turning Lathe.--Steelyard.--Rectangular Lever.--
Hammer.--Load between two Bearers.--Combination of Levers.--
Equivalent Lever. 167
CHAP. XIV.
OF WHEEL-WORK.
Wheel and Axle.--Thickness of the Rope.--Ways of applying the Power.
--Projecting Pins.--Windlass.--Winch.--Axle.--Horizontal Wheel.--
Tread-Mill.--Cranes.--Water-Wheels.--Paddle-Wheel.--Rachet-Wheel.--
Rack.--Spring of a Watch.--Fusee.--Straps or Cords.--Examples of.--
Turning Lathe.--Revolving Shafts.--Spinning Machinery.--Saw-Mill.--
Pinion.--Leaves.--Crane.--Spur-Wheels.--Crown-Wheels.--Bevelled
Wheels.--Hunting-Cog.--Chronometers.--Hair-Spring.--Balance-Wheel. 178
CHAP. XV.
OF THE PULLEY.
Cord.--Sheave.--Fixed Pulley.--Fire Escapes.--Single moveable
Pulley.--Systems of Pulleys.--Smeaton’s Tackle.--White’s Pulley.--
Advantage of.--Runner.--Spanish Bartons. 199
CHAP. XVI.
ON THE INCLINED PLANE, WEDGE, AND SCREW.
Inclined Plane.--Effect of a Weight on.--Power of.--Roads.--Power
Oblique to the Plane.--Plane sometimes moves under the Weight.--
Wedge.--Sometimes formed of two inclined Planes.--More powerful
as its Angle is acute.--Where used.--Limits to the Angle.--Screw.
--Hunter’s Screw.--Examples.--Micrometer Screw. 209
CHAP. XVII.
ON THE REGULATION AND ACCUMULATION OF FORCE.
Uniformity of Operation.--Irregularity of prime Mover.--Water-Mill.
--Wind-Mill.--Steam Pressure.--Animal Power.--Spring.--Regulators.
--Steam-Engine.--Governor.--Self-acting Damper.--Tachometer.--
Accumulation of Power.--Examples.--Hammer.--Flail.--Bow-string.--
Fire Arms.--Air-Gun.--Steam-Gun.--Inert Matter a Magazine for
Force.--Fly-Wheel.--Condensed Air.--Rolling Metal.--Coining-Press. 224
CHAP. XVIII.
MECHANICAL CONTRIVANCES FOR MODIFYING MOTION.
Division of Motion into rectilinear and rotatory.--Continued and
reciprocating.--Examples.--Flowing Water.--Wind.--Animal Motion.--
Falling of a Body.--Syringe-Pump.--Hammer.--Steam-Engine.--Fulling
Mill.--Rose-Engine.--Apparatus of Zureda.--Leupold’s Application
of it.--Hooke’s universal Joint.--Circular and alternate Motion.--
Examples.--Watt’s Methods of connecting the Motion of the Piston
with that of the Beam.--Parallel Motion. 245
CHAP. XIX.
OF FRICTION AND THE RIGIDITY OF CORDAGE.
Friction and Rigidity.--Laws of Friction.--Rigidity of Cordage.--
Strength of Materials.--Resistance from Friction.--Independent of
the Magnitude of Surfaces.--Examples.--Vince’s Experiments.--Effect
of Velocity.--Means for diminishing Friction.--Friction Wheels.--
Angle of Repose.--Best Angle of Draught.--Rail-Roads.--Stiffness
of Ropes. 260
CHAP. XX.
ON THE STRENGTH OF MATERIALS.
Difficulty of determining the Laws which govern the Strength of
Materials.--Forces tending to separate the Parts of a Solid.--Laws
by which Solids resist Compression.--Euler’s theory.--Transverse
Strength of Solids.--Strength diminished by the Increase of Height.
--Lateral or Transverse Strain.--Limits of Magnitude.--Relative
Strength of small Animals greater than large ones. 272
CHAP. XXI.
ON BALANCES AND PENDULUMS.
Weight.--Time.--The Balance.--Fulcrum.--Centre of Gravity of.--
Sensibility of.--Positions of the Fulcrum.--Beam variously
constructed.--Troughton’s Balance.--Robinson’s Balance.--Kater’s
Balance.--Method of adjusting a Balance.--Use of it.--Precautions
necessary.--Of Weights.--Adjustment of.--Dr. Black’s Balance.--
Steelyard.--Roman Statera or Steelyard.--Convenience of.--C. Paul’s
Steelyard.--Chinese Steelyard.--Danish Balance.--Bent Lever Balance.
--Brady’s Balance.--Weighing Machine for Turnpike Roads.--Instruments
for Weighing by means of a Spring.--Spring Steelyard.--Salter’s
Spring Balance.--Marriott’s Dial Weighing Machine.--Dynamometer.--
Compensation Pendulums.--Barton’s Gridiron Pendulum.--Table of linear
Expansion.--Second Table.--Harrison’s Pendulum.--Troughton’s
Pendulum.--Benzenberg’s Pendulum.--Ward’s Compensation Pendulum.--
Compensation Tube of Julien le Roy.--Deparcieux’s Compensation.--
Kater’s Pendulum.--Reed’s Pendulum.--Ellicott’s Pendulum.--Mercurial
Pendulum.--Graham’s Pendulum.--Compensation Pendulum of Wood and
Lead.--Smeaton’s Pendulum.--Brown’s Mode of Adjustment. 278
THE
ELEMENTS OF MECHANICS.
CHAP. I.
PROPERTIES OF MATTER--MAGNITUDE--IMPENETRABILITY--FIGURE--FORCE.
(1.) Placed in the material world, Man is continually exposed to the
action of an infinite variety of objects by which he is surrounded. The
body, to which the thinking and living principles have been united,
is an apparatus exquisitely contrived to receive and to transmit
impressions. Its various parts are organised with obvious reference to
the several external agents by which it is to be effected. Each organ
is designed to convey to the mind immediate notice of some peculiar
action, and is accordingly endued with a corresponding susceptibility.
This adaptation of such organs to the particular influences of
material agents, is rendered still more conspicuous when we consider
that, however delicate its structure, each organ is wholly insensible
to every influence except that to which it appears to be specially
appropriated. The eye, so intensely susceptible of impressions from
light, is not at all affected by those of sound; while the fine
mechanism of the ear, so sensitively alive to every effect of the
latter class, is altogether insensible to the former. The splendour of
excessive light may occasion blindness, and deafness may result from
the roar of a cannonade; but neither the sight nor the hearing can be
injured by the most extreme action of that principle which is designed
to affect the other.
Thus the organs of sense are instruments by which the mind is enabled
to determine the existence and the qualities of external things. The
effects which these objects produce upon the mind through the organs,
are called _sensations_, and these sensations are the immediate
elements of all human knowledge. MATTER is the general name which
has been given to that substance, which, under forms infinitely
various, affects the senses. Metaphysicians have differed in defining
this principle. Some have even doubted of its existence. But these
discussions are beyond the sphere of mechanical philosophy, the
conclusions of which are in nowise affected by them. Our investigations
here relate, not to matter as an abstract existence, but to those
qualities which we discover in it by the senses, and of the existence
of which we are sure, however the question as to matter itself may be
decided. When we speak of “bodies,” we mean those things, whatever they
be, which excite in our minds certain sensations; and the powers to
excite those sensations are called “properties,” or “qualities.”
(2.) To ascertain by observation the properties of bodies, is the
first step towards obtaining a knowledge of nature. Hence man becomes
a natural philosopher the moment he begins to feel and to perceive.
The first stage of life is a state of constant and curious excitement.
Observation and attention, ever awake, are engaged upon a succession
of objects new and wonderful. The large repository of the memory is
opened, and every hour pours into it unbounded stores of natural facts
and appearances, the rich materials of future knowledge. The keen
appetite for discovery implanted in the mind for the highest ends,
continually stimulated by the presence of what is novel, renders torpid
every other faculty, and the powers of reflection and comparison are
lost in the incessant activity and unexhausted vigour of observation.
After a season, however, the more ordinary classes of phenomena cease
to excite by their novelty. Attention is drawn from the discovery of
what is new, to the examination of what is familiar. From the external
world the mind turns in upon itself, and the feverish astonishment
of childhood gives place to the more calm contemplation of incipient
maturity. The vast and heterogeneous mass of phenomena collected by
past experience is brought under review. The great work of comparison
begins. Memory produces her stores, and reason arranges them. Then
succeed those first attempts at generalisation which mark the dawn of
science in the mind.
To compare, to classify, to generalise, seem to be instinctive
propensities peculiar to man. They separate him from inferior animals
by a wide chasm. It is to these powers that all the higher mental
attributes may be traced, and it is from their right application that
all progress in science must arise. Without these powers, the phenomena
of nature would continue a confused heap of crude facts, with which the
memory might be loaded, but from which the intellect would derive no
advantage. Comparison and generalisation are the great digestive organs
of the mind, by which only nutrition can be extracted from this mass of
intellectual food, and without which, observation the most extensive,
and attention the most unremitting, can be productive of no real or
useful advancement in knowledge.
(3.) Upon reviewing those properties of bodies which the senses
most frequently present to us, we observe that very few of them are
essential to, and inseparable from, matter. The greater number may be
called _particular_ or _peculiar qualities_, being found in some bodies
but not in others. Thus the property of attracting iron is peculiar to
the loadstone, and not observable in other substances. One body excites
the sensation of green, another of red, and a third is deprived of all
colour. A few characteristic and essential qualities are, however,
inseparable from matter in whatever state, or under whatever form it
exist. Such properties alone can be considered as tests of materiality.
Where their presence is neither manifest to sense, nor demonstrable by
reason, _there_ matter is not. The principal of these qualities are
_magnitude_ and _impenetrability_.
(4.) _Magnitude._--Every body occupies space, that is, it has
magnitude. This is a property observable by the senses in all bodies
which are not so minute as to elude them, and which the understanding
can trace to the smallest particle of matter. It is impossible, by any
stretch of imagination, even to conceive a portion of matter so minute
as to have no magnitude.
The _quantity_ of space which a body occupies is sometimes called its
_magnitude_. In colloquial phraseology, the word _size_ is used to
express this notion; but the most correct term, and that which we shall
generally adopt is _volume_. Thus we say, the volume of the earth is so
many cubic miles, the volume of this room is so many cubic feet.
The external limits of the magnitude of a body are _lines_ and
_surfaces_, lines being the limits which separate the several surfaces
of the same body. The linear limits of a body are also called _edges_.
Thus the line which separates the top of a chest from one of its sides
is called an edge.
The _quantity_ of a surface is called its _area_, and the _quantity_
of a line is called its _length_. Thus we say, the _area_ of a field
is so many acres, the _length_ of a rope is so many yards. The word
“magnitude” is, however, often used indifferently for volume, area,
and length. If the objects of investigation were of a more complex
and subtle character, as in metaphysics, this unsteady application of
terms might be productive of confusion, and even of error; but in this
science the meaning of the term is evident, from the way in which it is
applied, and no inconvenience is found to arise.
(5.) _Impenetrability._--This property will be most clearly explained
by defining the positive quality from which it takes its name, and
of which it merely signifies the absence. A substance would be
_penetrable_ if it were such as to allow another to pass through the
space which it occupies, without disturbing its component parts. Thus,
if a comet striking the earth could enter it at one side, and, passing
through it, emerge from the other without separating or deranging any
bodies on or within the earth, then the earth would be penetrable by
the comet. When bodies are said to be impenetrable, it is therefore
meant that one cannot pass through another without displacing some or
all of the component parts of that other. There are many instances of
apparent penetration; but in all these, the parts of the body which
seem to be penetrated are displaced. Thus, if the point of a needle be
plunged in a vessel of water, all the water which previously filled the
space into which the needle enters will be displaced, and the level of
the water will rise in the vessel to the same height as it would by
pouring in so much more water as would fill the space occupied by the
needle.
(6.) _Figure._--If the hand be placed upon a solid body, we become
sensible of its impenetrability, by the obstruction which it opposes to
the entrance of the hand within its dimensions. We are also sensible
that this obstruction commences at certain places; that it has certain
determinate limits; that these limitations are placed in certain
directions relatively to each other. The mutual relation which is found
to subsist between these boundaries of a body, gives us the notion of
its _figure_. The _figure_ and _volume_ of a body should be carefully
distinguished. Each is entirely independent of the other. Bodies having
very different _volumes_ may have the same _figure_; and in like manner
bodies differing in _figure_ may have the same _volume_. The figure of
a body is what in popular language is called its _shape_ or _form_. The
volume of a body is that which is commonly called its _size_. It will
hence be easily understood, that one body (a globe, for example) may
have ten times the volume of another (globe), and yet have the same
figure; and that two bodies (as a die and a globe) may have _figures_
altogether different, and yet have equal _volumes_. What we have here
observed of volumes will also be applicable to lengths and areas. The
arc of a circle and a straight line may have the same length, although
they have different figures; and, on the other hand, two arcs of
different circles may have the same figure, but very unequal lengths.
The surface of a ball is curved, that of the table plane; and yet the
_area_ of the surface of the ball may be equal to that of the table.
(7.) _Atoms--Molecules._--Impenetrability must not be confounded
with inseparability. Every body which has been brought under human
observation is separable into parts; and these parts, however small,
are separable into others, still more minute. To this process of
division no practical limit has ever been found. Nevertheless, many
of the phenomena which the researches of those who have successfully
examined the laws of nature have developed, render it highly probable
that all bodies are composed of elementary parts which are indivisible
and unalterable. The component parts, which may be called _atoms_, are
so minute, as altogether to elude the senses, even when aided by the
most powerful scientific instruments. The word _molecule_ is often used
to signify component parts of a body so small as to escape sensible
observation, but not ultimate atoms, each molecule being supposed to
be formed of several atoms, arranged according to some determinate
figure. _Particle_ is used also to express small component parts, but
more generally is applied to those which are not too minute to be
discoverable by observation.
(8.) _Force._--If the particles of matter were endued with no property
in relation to one another, except their mutual impenetrability, the
universe would be like a mass of sand, without variety of state or
form. Atoms, when placed in juxtaposition, would neither cohere, as in
solid bodies, nor repel each other, as in aeriform substances. On the
contrary, we find that in some cases the atoms which compose bodies
are not simply placed together, but a certain effect is manifested in
their strong coherence. If they were merely placed in juxtaposition,
their separation would be effected as easily as any one of them could
be removed from one place to another. Take a piece of iron, and
attempt to separate its parts: the effort will be strongly resisted,
and it will be a matter of much greater facility to move the whole
mass. It appears, therefore, that in such cases the parts which are in
juxtaposition _cohere_ and resist their mutual separation. This effect
is denominated _force_; and the constituent atoms are said to cohere
with a greater or less degree of force, according as they oppose a
greater or less resistance to their mutual separation.
The coherence of particles in juxtaposition is an effect of the same
class as the mutual approach of particles placed at a distance from
each other. It is not difficult to perceive that the same influence
which causes the bodies A and B to approach each other, when placed at
some distance asunder, will, when they unite, retain them together,
and oppose a resistance to their separation. Hence this effect of
the mutual approximation of bodies towards each other is also called
_force_.
Force is generally defined to be “whatever produces or opposes the
production of motion in matter.” In this sense, it is a name for
the unknown cause of a known effect. It would, however, be more
philosophical to give the name, not to the _cause_, of which we are
ignorant, but to the _effect_, of which we have sensible evidence.
To observe and to classify is the whole business of the natural
philosopher. When _causes_ are referred to, it is implied, that effects
of the same class arise from the agency of the same cause. However
probable this assumption may be, it is altogether unnecessary. All
the objects of science, the enlargement of mind, the extension and
improvement of knowledge, the facility of its acquisition, are obtained
by generalisation alone, and no good can arise from tainting our
conclusions with the possible errors of hypotheses.
It may be here, once for all, observed, that the phraseology of
causation and hypotheses has become so interwoven with the language
of science, that it is impossible to avoid the frequent use of it.
Thus, we say, “the magnet _attracts_ iron;” the expression _attract_
intimating the cause of the observed effect. In such cases, however,
we must be understood to mean the _effect itself_, finding it less
inconvenient to continue the use of the received phrases, modifying
their signification, than to introduce new ones.
Force, when manifested by the mutual approach or cohesion of bodies, is
also called _attraction_, and it is variously denominated, according to
the circumstances under which it is observed to act. Thus, the force
which holds together the atoms of solid bodies is called _cohesive
attraction_. The force which draws bodies to the surface of the earth,
when placed above it, is called the _attraction of gravitation_. The
force which is exhibited by the mutual approach, or adhesion, of the
loadstone and iron, is called _magnetic attraction_, and so on.
When force is manifested by the motion of bodies from each other, it
is called _repulsion_. Thus, if a piece of glass, having been briskly
rubbed with a silk handkerchief, touch successively two feathers, these
feathers, if brought near each other, will move asunder. This effect is
called _repulsion_, and the feathers are said to _repel_ each other.
(9.) The influence which forces have upon the form, state, arrangement,
and motions of material substances is the principal object of physical
science. In its strict sense, MECHANICS is a term of very extensive
signification. According to the more popular usage, however, it has
been generally applied to that part of physical science which includes
the investigation of the phenomena of motion and rest, pressure and
other effects developed by the mutual action of solid masses. The
consideration of similar phenomena, exhibited in bodies of the liquid
form, is consigned to HYDROSTATICS, and that of aeriform fluids to
PNEUMATICS.
CHAP. II.
DIVISIBILITY--POROSITY--DENSITY--COMPRESSIBILITY--ELASTICITY--DILATABILITY.
(10.) Besides the qualities of magnitude and impenetrability, there are
several other general properties of bodies contemplated in mechanical
philosophy, and to which we shall have frequent occasion to refer.
Those which we shall notice in the present chapter are,
1. Divisibility.
2. Porosity--Density.
3. Compressibility--Elasticity.
4. Dilatability.
(11.) _Divisibility._--Observation and experience prove that all bodies
of sensible magnitude, even the most solid, consist of parts which are
separable. To the practical subdivision of matter there seems to be no
assignable limit. Numerous examples of the division of matter, to a
degree almost exceeding belief, may be found in experimental enquiries
instituted in physical science; the useful arts furnish many instances
not less striking; but, perhaps, the most conspicuous proofs which can
be produced, of the extreme minuteness of which the parts of matter
are susceptible, arise from the consideration of certain parts of the
organised world.
(12.) The relative places of stars in the heavens, as seen in the
field of view of a telescope, are marked by fine lines of wire placed
before the eye-glass, and which cross each other at right angles. The
stars appearing in the telescope as mere lucid points without sensible
magnitude, it is necessary that the wires which mark their places
should have a corresponding tenuity. But these wires being magnified
by the eye-glass would have an apparent thickness, which would render
them inapplicable to this purpose, unless their real dimensions were of
a most uncommon degree of minuteness. To obtain wire for this purpose,
Dr. Wollaston invented the following process:--A piece of fine
platinum wire, _a b_, is extended along the axis of a cylindrical
mould, A B, _fig. 1._ Into this mould, at A, molten silver
is poured. Since the heat necessary for the fusion of platinum is much
greater than that which retains silver in the liquid form, the wire
_a b_ remains solid, while the mould A B is filled with
the silver. When the metal has become solid by being cooled, and has
been removed from the mould, a cylindrical bar of silver is obtained,
having a platinum wire in its axis. This bar is then wire-drawn, by
forcing it successively through holes C, D, E, F, G, H, diminishing
in magnitude, the first hole being a little less than the wire at
the beginning of the process. By these means the platinum _a b_
is wire-drawn at the same time and in the same proportion with the
silver, so that whatever be the original proportion of the thickness
of the wire _a b_ to that of the mould A B, the same will
be the proportion of the platinum wire to the whole at the several
thicknesses C, D, &c. If we suppose the mould A B to be ten times
the thickness of the wire _a b_, then the silver wire, throughout
the whole process, will be ten times the thickness of the platinum
wire which it includes within it. The silver wire may be drawn to a
thickness not exceeding the 300th of an inch. The platinum will thus
not exceed the 3000th of an inch. The wire is then dipped in nitric
acid, which dissolves the silver, but leaves the platinum solid. By
this method Dr. Wollaston succeeded in obtaining wire, the diameter of
which did not exceed the 18000th of an inch. A quantity of this wire,
equal in bulk to a common die used in games of chance, would extend
from Paris to Rome.
(13.) Newton succeeded in determining the thickness of very thin laminæ
of transparent substances by observing the colours which they reflect.
A soap bubble is a thin shell of water, and is observed to reflect
different colours from different parts of its surface. Immediately
before the bubble bursts, a black spot may be observed near the top. At
this part the thickness has been proved not to exceed the 2,500,000th
of an inch.
The transparent wings of certain insects are so attenuated in their
structure that 50,000 of them placed over each other would not form a
pile a quarter of an inch in height.
(14.) In the manufacture of embroidery it is necessary to obtain very
fine gilt silver threads. To accomplish this, a cylindrical bar of
silver, weighing 360 ounces, is covered with about two ounces of gold.
This gilt bar is then wire-drawn, as in the first example, until it
is reduced to a thread so fine that 3400 feet of it weigh less than
an ounce. The wire is then flattened by passing it between rollers
under a severe pressure, a process which increases its length, so that
about 4000 feet shall weigh one ounce. Hence, one foot will weigh the
4000th part of an ounce. The proportion of the gold to the silver in
the original bar was that of 2 to 360, or 1 to 180. Since the same
proportion is preserved after the bar has been wire-drawn, it follows
that the quantity of gold which covers one foot of the fine wire is the
180th part of the 4000th of an ounce; that is the 720,000th part of an
ounce.
The quantity of gold which covers one inch of this wire will be twelve
times less than that which covers one foot. Hence, this quantity will
be the 8,640,000th part of an ounce. If this inch be again divided
into 100 equal parts, every part will be distinctly visible without
the aid of microscopes. The gold which covers this small but visible
portion is the 864,000,000th part of an ounce. But we may proceed even
further; this portion of the wire may be viewed by a microscope which
magnifies 500 times, so that the 500th part of it will thus become
visible. In this manner, therefore, an ounce of gold may be divided
into 432,000,000,000 visible parts, each of which will possess all the
characters and qualities found in the largest masses of the metal.
It will retain its solidity, texture, and colour; it will resist the
same agents, and enter into combination with the same substances. If
the gilt wire be dipped in nitric acid, the silver within the coating
will be dissolved, but the hollow tube of gold which surrounded it will
still cohere and remain suspended.
(15.) The organised world offers still more remarkable examples of the
inconceivable subtilty of matter.
The blood which flows in the veins of animals is not, as it seems,
an uniformly red liquid. It consists of flat discs of a red colour,
floating in a transparent fluid called _serum_. In different species
these discs differ both in figure and in magnitude. In man and all
animals which suckle their young, they are perfectly circular or nearly
so. In birds, reptiles, and fishes, they are of oval form. In the human
species, the diameter of these discs is about the 3500th of an inch.
Hence it follows, that in a drop of blood which would remain suspended
from the point of a fine needle, there must be about 3,000,000 of such
discs.
Small as these discs are, the animal kingdom presents beings whose
whole bodies are still more minute. Animalcules have been discovered,
whose magnitude is such, that a million of them do not exceed the
bulk of a grain of sand; and yet each of these creatures is composed
of members as curiously organised as those of the largest species;
they have life and spontaneous motion, and are endued with sense and
instinct. In the liquids in which they live, they are observed to
move with astonishing speed and activity; nor are their motions blind
and fortuitous, but evidently governed by choice, and directed to an
end. They use food and drink, from which they derive nutrition, and
are therefore furnished with a digestive apparatus. They have great
muscular power, and are furnished with limbs and muscles of strength
and flexibility. They are susceptible of the same appetites, and
obnoxious to the same passions, the gratification of which is attended
with the same results as in our own species. Spallanzani observes, that
certain animalcules devour others so voraciously, that they fatten and
become indolent and sluggish by over-feeding. After a meal of this
kind, if they be confined in distilled water, so as to be deprived of
all food, their condition becomes reduced; they regain their spirit
and activity, and amuse themselves in the pursuit of the more minute
animals, which are supplied to them; they swallow these without
depriving them of life, for, by the aid of the microscope, the one
has been observed moving within the body of the other. These singular
appearances are not matters of idle and curious observation. They lead
us to enquire what parts are necessary to produce such results. Must we
not conclude that these creatures have heart, arteries, veins, muscles,
sinews, tendons, nerves, circulating fluids, and all the concomitant
apparatus of a living organised body? And if so, how inconceivably
minute must those parts be! If a globule of their blood bears the same
proportion to their whole bulk as a globule of our blood bears to our
magnitude, what powers of calculation can give an adequate notion of
its minuteness?
(16.) These and many other phenomena observed in the immediate
productions of nature, or developed by mechanical and chemical
processes, prove that the materials of which bodies are formed are
susceptible of minuteness which infinitely exceeds the powers of
sensible observation, even when those powers have been extended by all
the aids of science. Shall we then conclude that matter is infinitely
divisible, and that there are no original constituent atoms of
determinate magnitude and figure at which all subdivision must cease?
Such an inference would be unwarranted, even had we no other means of
judging the question, except those of direct observation; for it would
be imposing that limit on the works of nature which she has placed
upon our powers of observing them. Aided by reason, however, and a due
consideration of certain phenomena which come within our immediate
powers of observation, we are frequently able to determine other
phenomena which are beyond those powers. The diurnal motion of the
earth is not perceived by us, because all things around us participate
in it, preserve their relative position, and appear to be at rest. But
reason tells us that such a motion must produce the alternations of
day and night, and the rising and setting of all the heavenly bodies;
appearances which are plainly observable, and which betray the cause
from which they arise. Again, we cannot place ourselves at a distance
from the earth, and behold the axis on which it revolves, and observe
its peculiar obliquity to the orbit in which the earth moves; but we
see and feel the vicissitudes of the seasons, an effect which is the
immediate consequence of that inclination, and by which we are able to
detect it.
(17.) So it is in the present case. Although we are unable by direct
observation to prove the existence of constituent material atoms of
determinate figure, yet there are many observable phenomena which
render their existence in the highest degree probable, if not morally
certain. The most remarkable of this class of effects is observed in
the crystallisation of salts. When salt is dissolved in a sufficient
quantity of pure water, it mixes with the water in such a manner as
wholly to disappear to the sight and touch, the mixture being one
uniform transparent liquid like the water itself, before its union
with the salt. The presence of the salt in the water may, however, be
ascertained by weighing the mixture, which will be found to exceed
the original weight of the water by the exact amount of the weight
of the salt. It is a well-known fact, that a certain degree of heat
will convert water into vapour, and that the same degree of heat does
not produce the same effect upon salt. The mixture of salt and water
being exposed to this temperature, the water will gradually evaporate,
disengaging itself from the salt with which it has been combined. When
so much of the water has evaporated, that what remains is insufficient
to keep in solution the whole of the salt, a part of the latter thus
disengaged from the water will return to the solid state. The saline
constituent will not in this case collect in irregular solid molecules;
but will exhibit itself in particles of regular figure, terminated by
plane surfaces, the figure being always the same for the same species
of salt, but different for different species. These particles are
called _crystals_. There are several circumstances in the formation of
these _crystals_ which merit attention.
If one of them be detached from the others, and the progress of its
formation observed, it will be found gradually to increase, always
preserving its original figure. Since its increase must be caused
by the continued accession of saline molecules, disengaged by the
evaporation of the water, it follows that these molecules must be so
formed, that by attaching themselves successively to the crystal, they
maintain the regularity of its bounding planes, and preserve their
mutual inclinations unvaried.
Suppose a crystal to be taken from the liquid during the process of
crystallisation, and a piece broken from it so as to destroy the
regularity of its form: if the crystal thus broken be restored to the
liquid, it will be observed gradually to resume its regular form, the
atoms of salt successively dismissed by the vaporising water filling
up the irregular cavities produced by the fracture. Hence it follows,
that the saline particles which compose the surface of the crystal,
and those which form the interior of its mass, are similar, and exert
similar attractions on the atoms disengaged by the water.
All these details of the process of crystallisation are very evident
indications of a determinate figure in the ultimate atoms of the
substances which are crystallised. But besides the substances which are
thus reduced by art to the form of crystals, there are larger classes
which naturally exist in that state. There are certain planes, called
_planes of cleavage_, in the directions of which natural crystals are
easily divided. These planes, in substances of the same kind, always
have the same relative position, but differ in different substances.
The surfaces of the planes of cleavage are quite invisible before the
crystal is divided; but when the parts are separated, these surfaces
exhibit a most intense polish, which no effort of art can equal.
We may conceive crystallised substances to be regular mechanical
structures formed of atoms of a certain figure, on which the figure of
the whole structure must depend. The planes of cleavage are parallel to
the sides of the constituent atoms; and their directions, therefore,
form so many conditions for the determination of their figure. The
shape of the atoms being thus determined, it is not difficult to assign
all the various ways in which they may be arranged, so as to produce
figures which are accordingly found to correspond with the various
forms of crystals of the same substance.
(18.) When these phenomena are duly considered and compared, little
doubt can remain that all substances susceptible of crystallisation,
consist of atoms of determinate figure. This is the case with all solid
bodies whatever, which have come under scientific observation, for
they have been severally found in or reduced to a crystallised form.
Liquids crystallise in freezing, and if aëriform fluids could by any
means be reduced to the solid form, they would probably also manifest
the same effect. Hence it appears reasonable to presume, that all
bodies are composed of atoms; that the different qualities with which
we find different substances endued, depend on the magnitude and figure
of these atoms; that these atoms are indestructible and immutable by
any natural process, for we find the qualities which depend on them
unchangeably the same under all the influences to which they have been
submitted since their creation; that these atoms are so minute in their
magnitude, that they cannot be observed by any means which human art
has yet contrived; but still that magnitudes can be assigned which they
do not exceed.
It is proper, however, to observe here, that the various theorems
of mechanical science do not rest upon any hypothesis concerning
these atoms as a basis. These theorems are not inferred from this
or any other supposition, and therefore their truth would not be in
anywise disturbed, even though it should be established that matter is
physically divisible _in infinitum_. The basis of mechanical science
is _observed facts_, and, since the reasoning is demonstrative, the
conclusions have the same degree of certainty as the facts from which
they are deduced.
(19.) _Porosity._--The _volume_ of a body is the quantity of space
included within its external surfaces. The _mass_ of a body, is the
collection of atoms or material particles of which it consists. Two
atoms or particles are said to be in contact, when they have approached
each other until arrested by their mutual impenetrability. If the
component particles of a body were in contact, the _volume_ would be
completely occupied by the _mass_. But this is not the case. We shall
presently prove, that the component particles of no known substance are
in absolute contact. Hence it follows that the volume consists partly
of material particles, and partly of interstitial spaces, which spaces
are either absolutely void and empty, or filled by some substance of a
different kind from the body in question. These interstitial spaces are
called _pores_.
In bodies which are constituted uniformly throughout their entire
dimensions, the component particles and the pores are uniformly
distributed through the volume; that is, a given space in one part
of the volume will contain the same quantity of matter and the same
quantity of pores as an equal space in another part.
(20.) The proportion of the quantity of matter to the magnitude is
called the _density_. Thus if of two substances, one contain in a
given space twice as much matter as the other, it is said to be “twice
as dense.” The density of bodies is, therefore, proportionate to the
closeness or proximity of their particles; and it is evident, that the
greater the density, the less will be the porosity.
The pores of a body are frequently filled with another body of a more
subtle nature. If the pores of a body on the surface of the earth, and
exposed to the atmosphere, be greater than the atoms of air, then the
air may pervade the pores. This is found to be the case with many sorts
of wood which have an open grain. If a piece of such wood, or of chalk,
or of sugar, be pressed to the bottom of a vessel of water, the air
which fills the pores will be observed to escape in bubbles and to rise
to the surface, the water entering the pores, and taking its place.
If a tall vessel or tube, having a wooden bottom, be filled with
quicksilver, the liquid metal will be forced by its own weight through
the pores of the wood, and will be seen escaping in a silver shower
from the bottom.
(21.) The process of filtration, in the arts, depends on the presence
of pores of such a magnitude as to allow a passage to the liquid, but
to refuse it to those impurities from which it is to be disengaged.
Various substances are used as filtres; but, whatever be used, this
circumstance should always be remembered, that no substance can be
separated from a liquid by filtration, except one whose particles
are larger than those of the liquid. In general, filtres are used to
separate _solid_ impurities from a liquid. The most ordinary filtres
are soft stone, paper, and charcoal.
(22.) All organised substances in the animal and vegetable kingdoms
are, from their very natures, porous in a high degree. Minerals are
porous in various degrees. Among the silicious stones is one called
_hydrophane_, which manifests its porosity in a very remarkable manner.
The stone, in its ordinary state, is semi-transparent. If, however,
it be plunged in water, when it is withdrawn it is as translucent
as glass. The pores, in this case, previously filled with air, are
pervaded by the water, between which and the stone there subsists
a physical relation, by which the one renders the other perfectly
transparent.