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Title: A Treatise on Mechanics Author: Henry Kater and Dionysius Lardner Release Date: August 17, 2021 [eBook #66078] Language: English Character set encoding: UTF-8 Produced by: Thiers Halliwell, deaurider and the Online Distributed Proofreading Team at https://www.pgdp.net (This file was produced from images generously made available by The Internet Archive) *** START OF THE PROJECT GUTENBERG EBOOK A TREATISE ON MECHANICS *** Transcriber’s notes: The text of this e-book has mostly been preserved in its original form including some inconsistency of hyphenation and use of diacritics (aeriform/aëriform). Three spelling typos have been corrected (arrangment → arrangement, pully → pulley, dye → die) as have typos in equations on pages 40 and 43. And some missing punctuation has been corrected silently (periods, commas, incorrect quotes). To assist the reader, hyperlinks have been added to the table of contents, index and footnotes, as well as to the numerous cross-references within the text. Page numbers are shown in the right margin and footnotes are located at the end. 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. 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 Gener‐ alisation.—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.— Hypo​thet​ical Phrases un​neces​sary.—At​trac​tion. 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.—Por‐ osity.—Volume.—Density. —Quicksilver passing through Pores of Wood.—Filtration.—Por‐ osity of Hydrophane. —Compressibility.—Elasticity.—Dilatability.—Heat.—Contraction of Metal used to restore the Perpendicular to Walls of a Building.—Impenetrability of Air. —Compressibil‐ ity of it.—Elasticity of it.—Liquids not absolutely incompressible. —Experiments.—Elasticity of Fluids.—Aeri​form Fluids.—Do​mes​tic Fire Box.— Evo​lu​tion of Heat by com​pressed 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 Con​se​quen​ces 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.—Ab​so​lute and rela​tive Motion. 48 CHAP. VI. ATTRACTION. Impulse.—Mechanical State of Bodies.—Absolute Rest.—Uniform and rectilinear Motion.—Attrac‐ tions.—Molecular or atomic.—Interstitial Spaces in Bodies.—Repulsion and Attraction.—Cohe‐ sion.—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 Hydro‐ gen. —Oxygen and Quicksilver.—Magnetism.—Electricity and Electro-Magnetism.—Gravita‐ tion.—Its Law.—Examples of.—Depends on the Mass.—Attraction between the Earth and de‐ tached Bodies on its Surface.—Weight.—Gravitation of the Earth.—Illustrated by Projectiles. — Plumb-Line.—Caven​dish’s Experi​ments. 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.—Princi‐ ples of uniformly accelerated Motion.—Relations between the Height, Time, and Velocity.— Attwood’s Machine.—Re​tard​ed 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 v vi Motion down a Curve.—Depends upon Velocity and Curvature.—Centrifugal Force.—Circle of Curvature.—Radius of Curvature.—Whirling Table.—Experiments.—Solar System.—Examples of centri​fugal 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 some​times 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 con‐ tinued Forces.—Percussion.—Continued Force.—Rotation.—Impressed Forces.—Properties of a fixed Axis.—Movement of the Force round the Axis.—Leverage of the Force.—Impulse per‐ pendicular to, but not crossing, the Axis.—Radius of Gyration.—Centre of Gyration.—Moment of Iner​tia.—Prin​ci​pal Axes.—Centre of Per​cus​sion. 128 CHAP. XI. OF THE PENDULUM. Isochronism.—Experiments.—Simple Pendulum.—Examples illustrative of.—Length of.—Experi‐ ments of Kater, Biot, Sabine, and others.—Huygens’ Cyc​loi​dal Pen​du​lum. 145 CHAP. XII. OF SIMPLE MACHINES. Statics.—Dynamics.—Force.—Power.—Weight.—Lever.—Cord.—In​clined 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.— Com​bin​ation of Levers.—Equi​va​lent 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.— Chro​no​meters. —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.—Ad​van​tage 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.—Mi​cro​meter Screw. 209 CHAP. XVII. ON THE REGULATION AND ACCUMULATION OF FORCE. Uniformity of Operation.—Irregularity of prime Mover.—Water-Mill.—Wind-Mill.—Steam Press‐ ure.—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.—Roll​ing Metal.—Coin​ing-Press. 224 CHAP. XVIII. MECHANICAL CONTRIVANCES FOR MODIFYING MOTION. Division of Motion into rectilinear and rotatory.—Con​tinued and re​cip​ro​ca​ting.—Examples.—Flow​‐ vii viii Division of Motion into rectilinear and rotatory.—Con​tinued and re​cip​ro​ca​ting.—Examples.—Flow​‐ ing 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 con‐ nect​ing the Motion of the Pis​ton with that of the Beam.—Para​llel Motion. 245 CHAP. XIX. OF FRICTION AND THE RIGIDITY OF CORDAGE. Friction and Rigidity.—Laws of Friction.—Rigidity of Cordage.—Strength of Materials.—Resist‐ ance from Friction.—Independent of the Magnitude of Surfaces.—Examples.—Vince’s Experi‐ ments.—Effect of Velocity.—Means for diminishing Friction.—Friction Wheels.—Angle of Repose.—Best Angle of Draught.—Rail-Roads.—Stiff​ness of Ropes. 260 CHAP. XX. ON THE STRENGTH OF MATERIALS. Difficulty of determining the Laws which govern the Strength of Materials.—Forces tending to se‐ parate 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 Steel-yard.—Danish Balance.—Bent Lever Bal‐ ance.—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 Pendu‐ lum.—Mercurial Pendulum.—Graham’s Pendulum.—Compensation Pendulum of Wood and Lead.—Smeaton’s Pen​du​lum.—Brown’s Mode of Ad​just​ment. 278 THE ELEMENTS OF MECHANICS. ix 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 2 3 4 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 5 6 7 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. 8 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. 9 10 11 12 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 13 14 15 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 16 17 18 perfectly transparent. Larger mineral masses exhibit degrees of porosity not less striking. Water percolates through the sides and roofs of caverns and grottoes, and being impregnated with calcareous and other earths, forms stalactites, or pendant protuberances, which present a curious appearance. (23.) Compressibility.—That quality, in virtue of which a body allows its volume to be diminished without diminishing its mass, is called compressibility. This effect is produced by bringing the constituent particles more close together, and thereby increasing the density and diminishing the pores. This effect may be produced in several ways; but the name “compressibility” is only applied to it when it is caused by the agency of mechanical force, as by pressure or percussion. All known bodies, whatever be their nature, are capable of having their dimensions reduced without diminishing their mass; and this is one of the most conclusive proofs that all bodies are porous, or that the constituent atoms are not in contact; for the space by which the volume may be diminished must, before the diminution, consist of pores. (24.) Elasticity.—Some bodies, when compressed by mechanical agency, will resume their former dimensions with a certain energy when relieved from the operation of the force which has compressed them. This property is called elasticity; and it follows, from this definition, that all elastic bodies must be compressible, although the converse is not true, compressibility not necessarily implying elasticity. (25.) Dilatability.—This quality is the opposite of compressibility. It is the capability observed in bodies to have their volume enlarged without increasing their mass. This effect may be produced in several ways. In ordinary circumstances, a body may exist under the constant action of a pressure by which its volume and density are determined. It may happen, that on the occasional removal of that pressure, the body will dilate by a quality inherent in its const...