1.1. From the Preface.

In a Treatise intended for the purposes of Academical instruction it is of the first importance that the more elementary propositions should be laid down, reference being had only to the simplest and most obvious methods of investigation.

The attainment of this object has in the following work been found in some degree incompatible with a strictly scientific arrangement of its parts.

The discussion of the general equations of Equilibrium evidently forms the legitimate basis of a theory of Hydrostatics. This discussion involves however the consideration of a point in space referred to three rectangular co-ordinates, and is, in its most general form, by no means essential to a further progress in the subject: it has therefore been referred to the end of the work, and that particular case of it in which the accelerating force is gravity, considered alone.

In the theory of the motion of fluids, a distinction has been made between the case in which the velocity of every particle is the same as it passes through the same point in space; and the more extended case of variable motion. Of the former a separate solution has been obtained; and on the resulting formula the whole of the theory of Hydrodynamics has been made to depend. The manner in which this part of the subject has been treated is believed to be altogether new.

It is unnecessary here to enter further into the arrangement of the work. The reader is referred to a copious table of Contents which has been prefixed to it.

In conclusion the Author has to acknowledge his important obligations to his friend Mr Challis, of Trinity College. He is indebted to that Gentleman for the Chapter (VII) on the general Equations of the Motion of Fluids, and the Appendix (A) on the Oscillations of a cylindrical Column of Air. In the former of these papers, Mr Challis has completely solved the general equation expressing the continuity of a moving fluid.

West Monkton, near Taunton,
30 March 1830.

2.1. Initial material.

To Be Delivered At The King's College, London, in The October Term of the year 1831 by Rev H Moseley, Professor of Natural and Experimental Philosophy.

These Lectures require no introductory course of mathematical reading; the method of demonstration being exclusively experimental.

2.2. Beginning of the 38-page Syllabus.

Time. - Space. - Matter. - Force.
On the nature of a Property or Quality.

The Properties of Matter. - Impenetrability - uselessness of the term, as simply implying the distinction of matter and space. - Divisibility.
Molecules. - Quantity. - Motion . - Force. - Quantity of motion.-Velocity. - Direction. - Resistance. - Pressure. - Equilibrium.

All the mutual relations of Time - Space - Matter - and Force, belong properly to the science of Mechanics.
According to the usual acceptation of the term, Mechanics, that science is, however, confined to the investigation of the conditions of the equilibrium and the motion of masses, or aggregates of matter, acted upon by known and appreciable forces.

To the theory of Equilibrium belong - the science of Statics, or the Equilibrium of Solids - and the science of Hydrostatics, or the Equilibrium of
Fluids.

To the theory of Motion belong - the science of Dynamics, or the Motion of Solids - and of Hydrodynamics, or the Motion of Fluids.

On the Abstract or Mathematical Method in Physics.

On the Experimental Method - Nature and limits of the proof by experiment.

3.1. From the Preface.

The following work contains treatises on the sciences of Statics and Hydrostatics, comprising the whole theory of Equilibrium. It was intended as the first volume of a course of Natural Philosophy, for the use of those who have no knowledge of Mathematics, or who have made but little progress in their mathematical reading.

The Theoretical principles of Statics are comprised in the First Three Chapters of the work; the remaining chapters contain little more than a practical application of these principles.

It is impossible to arrange the parts of a demonstrative science in the order of their difficulty; these first chapters will probably be found to present more difficulties to the student than any other portion of the work. A thorough knowledge of the elementary principles discussed in them, is, nevertheless, a necessary introduction to the more practical parts of the science of Mechanics.

Into every practical question of equilibrium, there enters the consideration of weight; the mass held in equilibrium, whatever other forces may be applied to it, being necessarily subject to the action of the force of Gravity.

A discussion of the influence of the weight acting in every portion of the mass of a body, upon the conditions of its equilibrium; and of the properties of its centre of gravity through which this weight may be supposed, in every position of the body, to act; constitutes, therefore, the subject of the next, or Fourth Chapter of the work.

There is scarcely any case of equilibrium, among the forces com posing which, there do not enter two or more resistances of the surfaces of bodies in contact. The question of the resistances of the surfaces of bodies, constitutes, therefore, the subject of the Fifth Chapter. The method of treating it is altogether new.

It is shown, that force applied to the surface of one body by the intervention of the surface of another, is destroyed, however great it maybe, provided its direction lie within a certain right cone; having its vertex at the point of contact, and its axis perpendicular to the touching surfaces: and that it is not destroyed, however small it may be, provided its direction lie without that cone.

It is by means of this property, that allowance is made for what is usually termed, friction - which is in reality, no other than the difference of the case of the resistance of a surface, as it actually obtains in nature, from the hypothetical case of resistance only in the direction of a normal: which hypothetical case, introduced in the infancy of the science, and intended to facilitate its first deductions, has been most unaccountably retained as a principle of equilibrium.

The nature and properties of the forces from whence the equilibrium of material bodies commonly results, having been thus ascertained, the next Eight Chapters present the application of these to the Inclined Plane, the Wedge, the Lever, the Wheel and Axle, the Screw, and the Pulley; usually termed the Mechanical Powers.

Chapters Fourteen and Fifteen contain the theory of the equilibrium of systems of variable form. It is shown, that the conditions of the equilibrium of a rigid system are necessary to the equilibrium of the same system, when made to admit of variation in its form, but not sufficient. And from this principle are deduced certain conditions of the equilibrium of polygons and frames of rods and cords, of the catenary, and finally, the conditions of the equilibrium of bodies in contact, including the Arch.

Chapter Sixteen contains a Discussion, of Dr Young's theory of the
strength of materials, and a table of moduli of elasticity and extension.

In Chapter Eighteen, will be found Lagrange's celebrated Demonstration of the principle of Virtual Velocities, which it has been attempted to bring within the comprehension of ordinary readers; and Chapter Nineteen, which contains the theory of Resistances and a demonstration of the new principle of Least Resistance, completes the theory of Statics.

The theory of Hydrostatics or the Equilibrium of Fluid Bodies, presents the extreme case of the equilibrium of a system of variable form. Any portion of such a fluid mass in equilibrium, is therefore subject to the same conditions, as though it were a solid; together with such other conditions as result from its fluidity. It is on this principle, that the whole theory of Hydrostatics is built.

In the First Chapter is discussed the principle of the equal distribution of fluid pressure; in the Second, the conditions of the equilibrium of a heavy fluid; in the Third, the oblique pressure of a heavy fluid, the forms of embankments, the centre of pressure, &c.; the Fourth Chapter treats of the conditions of the equilibrium of floating bodies; the Fifth, of specific gravity, and the instruments used for determining it: and the last, treats of the Science of Pneumatics, or the Equilibrium of Elastic Fluids, and the Hydraulic Instruments dependent upon it.

Throughout the whole, an attempt has been made to bring the principles of exact science to bear upon questions of practical application in the arts, and to place the discussion of these within the reach of the more intelligent of that useful class of men who are connected with the manufactures of the country.

The Author has to acknowledge his obligations to the work of M Dupin, entitled Méchanique appliquée aux Arts, for several of the illustrations of the Parallelogram of Forces, and the Centre of Gravity; and to the popular work of Dr Lardner on Hydrostatics, for the rules stated to be those which govern the relation of the changes of the barometer, to the changes of the weather.

3.2. Note.

The 3rd edition, published in 1847, has "Rev H Moseley, M.A F.R.S., one of Her Majesty's Inspectors of Schools; Late Professor of Natural Philosophy and Astronomy, King's College, London; Author of Lectures on Astronomy, etc."

4.1. Advertisement.

This work originally formed part of a course of Lectures delivered to the Class of Natural Philosophy and Astronomy, at King's College. They were subsequently printed in the Magazine of Popular Science, and have since been revised by the Author, and adapted for publication in a separate volume, in the belief that it may serve the purposes of Popular Instruction.

4.2. From the Introduction.

There can have been no period in the history of man kind in which they did not behold, with a desire to comprehend them, the changes which are daily taking place in the face of the heavens above them; and there can have been none in which they did not perceive these changes to sympathize with others in the surface of the earth around them. He who looks out upon the heavens, beholds a canopy spread forth like the half of a great sphere, of which he appears to occupy the centre. In the day-time, when it is of the colour of the azure, - the hue of light in which his perception of its existence is most pleasant to him, - the sun daily takes his course, in a zone, across this fair canopy, "like a giant that renews his strength." As night approaches, the curtain of the heavens gradually loses its transparent blueness, becomes opaque, darkens, and at length it is black as sackcloth of hair; then come the millions of the stars, which are strewed like gems upon its surface; and in her season the moon walks forth in her brightness, and holds sway amid the dreary watches of the night. These daily changes in the heavens have but little apparent relation to the changes of vegetable life, but over the whole of the animated creation their power is manifest. The song of the birds becomes mute at nightfall, and again wakes only to welcome the returning sun. The beast lies down in the forest, the reptile crawls to his lair, and man himself sinks under the mysterious influence of the changing heavens; and returning to a state, the image of that state of oblivion out of which his birth first brought him, he stretches himself out to sleep. Such is the experience of a day. That of a year brings a still further knowledge of the wonderful sympathy between the changes in the heavens above him, and those in the things around him. He sees the sun not daily to describe the same path in the heavens, but at one time to travel obliquely across them in a higher, and at another time in a lower zone, so as at one time to have a longer course to run, and at another a shorter; and thus at one time to give him a longer, and at another a shorter day. This change in the elevation and consequent length of the sun's oblique path in the heavens, he soon perceives to be coupled with a change in his own perceptions of the intensity of heat and cold; when the sun's path is lowest or most oblique, he is colder than when it is highest. And not only do his own feelings sympathize with this change, but all nature around him. The hand that covered the beast of the forest with a coat of fur, in the winter thickens its garment. The bird, whose path is free in the heavens, then, guided by a spark of that intelligence which called it into being, becomes conscious of the existence of a warmer sky in some remote unseen region of the earth, and seeks it. The green herb withers, the blossom dies, the leaf becomes sapless, and falls to the ground. Is it possible, that he who beholds all these changes around him, and who is thus deeply interested in them, who cannot but see that they are all bound together as by a chain, and made to sympathize with one another, should not seek to trace out still more of the mystery of their union, to know more of its nature and laws, and to unravel its cause?

Man is necessarily, and from the very mode and nature of his existence, a speculative being. And of all subjects of speculation, the changes in the heavens are probably those which first arrested his attention. How earnestly, for instance, must the master spirits of those days, when the secret of the universe was unknown, have wished and have laboured to account for the phenomena which we now so readily explain, by means of our knowledge of the form of the earth: how must the mysterious alternation of day and night, and the march of the seasons, have distracted them, wearied their imaginations, and perplexed their reasonings.

Quae mare compescantcausae; quid temperet annum;
Stellae sponte sua, jussaene vagentur et errent;
Quid premat obscurum lunae, quid proferat orbem;
Quid velit et possit rerum concordia discors.

It was in these words that Horace described the sublime but very unsatisfactory speculations of his friend Grosphus.

The mighty changes in the heavens controlling, as they do, all the phenomena of animal and vegetable life, necessarily couple themselves in the mind with the direct agency of the supernatural world, and thus it was that the astronomy of the ancients became incorporated with their mythology. And thus, "the history of the development of the religious principle among them, was little other than a history of the wanderings and uncertainties of the human understanding, which, placed in a world it could not comprehend, sought, nevertheless, with unwearied solicitude to develop the secret of it; which, a spectator of the mysterious and visible prodigy of the universe, imagined causes for it, supposed objects, and raised up systems; which, finding one defective, destroyed it to raise another not less faulty on its ruins; which abhorred the errors that it renounced, misunderstood those which it embraced; repulsed the very truth for which it sought; conjured up chimeras of invisible agents, and dreaming on, without discretion and without happiness, was at length utterly bewildered in a labyrinth of illusions."

How great is the contrast! Since the age in which the heathen mythology had its origin, the religion of man kind has fixed itself upon the sure foundation of a revelation from God, and the human understanding has acquired for itself the master secret of the universe. The wanderings of the stars on the firmament of the heavens are at length understood. The question

Sponte sua jussaene vagentur et errent?

no longer perplexes us. We find in what appeared to our ancestors the capricious motions of powerful but isolated beings, evidences of one impulse, one will, one design, one Almighty power, originating, sustaining, and controlling the whole. These beings then, to whom, calling them their gods, it was natural that they should attribute a separate, independent, and capricious existence, subject to the indecision, the error, and the feebleness of humanity, appear to us but as the creatures of one sovereign intelligence, bound down in as passive obedience to that intelligence, as the stone that falls from the hand, or the apple that falls from the tree; with no other thought, or will, or power, than that of any particle of dust blown about by the Summer's wind. Thus the whole of the sublime and gorgeous pageantry of the heathen mythology vanishes like the baseless fabric of a dream.

We know that this magnificent phantom retained its shadowy control over the intellect of man, in an age of great literary refinement, of profound knowledge in the philosophy of morals, and of high civilization; and had no revelation interposed, there could be nothing found in the mere literature, ethics, and civilization of our day, as distinguished from the literature, ethics, and civilization of theirs, to over throw it; thus we might still, in respect to these, be what we are, and yet the worshippers of a host of gods: but combine with these the science of our times, and the sup position becomes impossible; a single ray penetrating the mystery of the universe is sufficient to dispel the illusion of Polytheism.

How prodigious has been the progress which the universal mind of man has since made, how wonderful the vantage ground on which we stand, when we look forth upon nature. In comparison with that time of its infancy, the human intellect now walks to and fro in creation, as with the strength of a giant, the growth of whose stature has been through ages and who is yet removed by an interval of ages from the noontide of his vigour. In this introduction the truths of natural science have been spoken of with a direct reference to the wisdom, the power, and the goodness of the Author of Nature, and references of a like kind will be found in the course of the work. This is done advisedly, and from the belief that a course of instruction cannot be Complete, which, having for its object the development of the relation of cause and effect in those portions of the sequence of natural things which lie within the scope of sensation, does not, at least, point out their dependence upon that great First Cause which is beyond it - and that, were it not an impiety to discuss the manifestations of infinite wisdom and goodness in created things, otherwise than with sentiments of gratitude to the Creator, and with deep humility before him, it could at least be considered but as an affectation or a folly. The study of Natural Philosophy and of Natural Theology, if rightly pursued, are, in reality, one; and true Science but a perpetual worship of God in the firmament of his power.

The first question which suggests itself to a mind curious to understand the phenomena of the heavens, is probably this - Are the Sun, Moon, Planets, and Stars really as they seem to be, at the same distance from us, and almost within our reach? or are they, as we are told, some of them in finitely more remote from us than others; and the nearest of them distant more than half a million of miles? Our first inquiry shall then be "What is the probable Distance of the Fixed Stars?"

4.2. Later editions.

A Second edition was published in 1846, a Third revised edition in 1850, and a Fourth revised edition in 1854. later editions give Henry Moseley as one of the Inspectors of Schools aided by Public Grants; Late Professor of Natural Philosophy and Astronomy, King's College, London; author of A treatise in Mechanics Applied to the Arts.

5.1. From the Introduction.

This work is the first of a series, entitled Illustrations of Science, by Professors of King's College, London, to be published at intervals of three months, and continued until the circle of the Physical Sciences, and the Sciences of Observation, is embraced in it. The author has proposed to himself the development of that system of experimental facts and theoretical principles on which the whole superstructure of mechanical art may be considered to rest, and its introduction, under an available form, to the great business of practical education. To effect this object, and to reconcile, as far as it may be possible, the strictly scientific with the popular and elementary character of the undertaking, a new method has been sought, the nature of which is sufficiently indicated by its title - Illustrations of Mechanics. The work consists, in fact, of a series of illustrations of the science of mechanics, arranged in the order in which the parts of that science succeed each other, and connected by such explanations only, as may serve to carry the mind on from one principle to another, and enable it to embrace and combine the whole - a plan which leaves to the author the selection of such elements only of his science as are capable of popular illustration, and as come within the limits of practical instruction; and which enables him to exclude from his work all abstract reasoning, and mathematical deduction.

Throughout, an attempt is made to give to the various illustrations an entirely elementary and practical character; and each illustration forming a short distinct article, the subject of which is enunciated at the commencement of it, the work has assumed a broken form, adapted peculiarly, it is conceived, to the purposes of scholastic instruction.

It is an idea which presents itself to the mind of every man who has children to educate and provide for, which is a constant subject of comment and discussion, and which prevails through all classes of society, that a portion of the school life of a boy ought to be devoted to the acquisition of those general principles of practical knowledge of which the whole business of his subsequent life is to form a special application; that there ought, in fact, to be commenced by him at school a common apprenticeship to those great elements of knowledge, on which hang all the questions of interest which are to surround him in nature, and which are destined, under the form of practical science, to take an active share in the profession, trade, manufacture, or art, whatever it may be, which is hereafter to become the occupation of his life.

It is the object of this work, and of the Series of which it forms part, to promote this great business of Practical Education, by supplying to the instructors of youth a system of elementary science, adapted to the ordinary forms of instruction. No one can doubt that the same capabilities in the scholar, united to the same zeal in the master, which now suffice to carry the elements of a classical education to the very refinements of philological criticism, would be equal to the task of instruction in the nomenclature of the physical sciences, their fundamental experiments, their elementary reasonings, and their chief practical results; nor can it be questioned that the ordinary intelligence of youth, and common diligence on the part of their teachers, would enable them to master the secrets of the more important of the arts, and the chief processes of the manufactures; and would place within their reach the elements of natural history, the general classification of the animal and vegetable kingdoms of nature, and their various ministries to the uses of man.

These are elements of a knowledge which is of inestimable value in the affairs of life; and the interests of this great commercial and manufacturing community claim that they should no longer be left to find their way to the young mind (if, indeed, they reach it at all) rather as a relaxation of the graver business of education than as a part of it.

That instruction which does not unite with all other knowledge the knowledge of those great truths of religion on which rests, as its foundation, the fabric of human happiness, can at best be considered but as a questionable gift. As a work of education, therefore, any treatise which, having for its object the development of principles of natural knowledge, did not point to the great Author of nature, would be an imperfect work; and, more than this, such a work, considered in a scientific point of view, would assuredly bear on its face a blemish; for, were it not an impiety to discuss the infinite manifestation of wisdom and goodness in creation otherwise than with sentiments of reverence to the Creator, and deep humility before him, it could at best be considered but as an affectation and a folly. It is under the influence of this conviction that, in the following work, the laws of the natural world have been taught - where the opportunity has been presented - with a direct reference to the power, the wisdom, and the goodness of God.

The illustrations of the mechanical properties of matter and the laws of force are drawn promiscuously and almost equally from Art and Nature.

It is not by design that examples taken from these distinct sources thus intermingle, but simply because they suggest themselves as readily from the one source as the other - from nature as abundantly as from art.

An important truth is shadowed forth in this fact.

There is a Relation between Art and Nature - a relation amounting to more than a resemblance; - a relation by which the eye of the practical man may be guided to that God who works with him in every operation of his skill, and mechanical art elevated from a position which is sometimes unjustly assigned to it among the elements of knowledge. It cannot be misplaced in this commencement of a work, which has for its object to develop the great principles of natural science, and which bears upon its title the arms and the motto of an institution formed to unite instruction in the precepts of religious knowledge with the elements of human learning, to point out this relation. The following illustration will serve the purpose, and will assimilate with the general method of the work:

I take up a work of art, I examine it, I see on it stamped the evidence of the power and skill, the judgment and knowledge, of the maker: there is the evidence of design in it, there is proof of the economy of labour - its material is suited for its use, and as little of it as possible is used, and its form is controlled by a perception, however imperfect, of the beauty and regularity of form. These are things, the evidence of which I perceive in the thing itself. It matters not that I saw it not made, - that I know not the maker - that he has never instructed me in the secret of his art: for centuries he may have been dead, and may have left no record of the manner of his working.

This matters not, I see plainly the design with which he wrought. The thoughts of his mind rise up before mine as though I were present to them - stamped upon it are the traces of intelligence, power, and skill, which have operated in its formation - invisible things - no hand any longer works in it - no skill has any longer its visible exercise in it - no name is inscribed upon it - no legend records for me the fact that there wisdom, knowledge, and power, were exercised - yet is the existence of these things, and their exercise in that work of art, among the most certain elements of my knowledge: my reason claims for me the admission of these among the most certain of the things that I may know, deduced by no new or unaccustomed operation of my mind, but by processes of thought which I am daily in the habit of verifying.

Now let me take up a work of nature, and place it beside that thing of art. Evidence such as that which I have found in the artificial thing is to be sought only in the thing itself, and essentially belongs to it. I may seek it then in this work of nature, as in that of art, and it may, or it may not, be found here, as it was found there. - By every mark and sign that I judged of that work of art I judge of this of nature - every rule, which I applied to the one, I apply to the other; and the conclusion which I draw from the one, with a certainty that never, as I know by experience, fails me, I draw with equal certainty from the other.

Is there in the work of art the evidence of means to an end? I behold the very same evidence in the work of nature. Is there an adaptation of the material, in the one case? there is the like in the other. Is the artificial thing collected and arranged as to al its elements for a specific object, to which each element is made subordinate? so is the natural thing. Is the contrivance of the one complicated, involving many subsidiary contrivances, all having their direction towards an ultimate result? so is that of the other. Does the work of art manifest an economy of material and of labour in its construction? there is the like economy apparent in the work of nature. Subject to the adaptation of the form of the artificial thing to its use, and to the economy of its material, and the labour bestowed upon it, is the disposition of its parts governed by a certain perception of beauty and of grace - who shall describe the beauty of nature?

The only difference is, indeed, this, that in the work of nature all these qualities exist in their infinite perfection - in the work of art, in their infinite imperfection. The evidence is perfectly alike in kind, although it is the evidence of things infinitely remote in degree.

With whatever certainty, then, I reason of the finite wisdom and power of the artificer from that work of his art, with the same certainty do I reason of the infinite wisdom and power of the eternal God from the works of his hand; and on this evidence I declare with St Paul, that "the invisible things of him from the beginning of the world are manifest, being plainly seen by the things which are made, even his eternal power and Godhead." (Rom .i.20.).

Every work of human art or skill is a thing done by a creature of God; a creature Made in His Own Image, and operating upon matter governed by the same laws, which He, in the beginning, infixed in it, and to which he subjected the first operations of his own hands - a creature in whom is implanted reason of alike nature with that excellent wisdom by which the heavens were stretched forth - living power as that of a worm, and as a vapour that passeth away, but an emanation of Omnipotence - a perception of beauty and adaptation akin to that whence flowed the magnificence of the universe - and to control these, a volition, whose freedom has its remote analogy and its source in that of the first self-existent and independent Cause.

It is from this relation between the Author of nature and the being in whom the works of art have their origin that arise those relations, infinitely remote, but distinct, between the things themselves, of which the evidence is every where around us. These are necessary relations: it is not that the works of art are made by any purpose or intention in the resemblance of those of nature, or that there is any unseen influence of nature itself upon art - the primary relation is in the causes whence these severally proceed.

Thus it is possible, that in the infinities of nature, every thing in art may find its type; this is not, however, necessarily the case, since the causes are infinitely removed, since, more over, in their operation, these causes are in dependent, and since nature operates upon materials which are not within the resources of art.

How full of pride is the thought, that in every exercise of human skill, in each ingenious adaptation, and in each complicated contrivance and combination of art, there is included the exercise of a faculty which is akin to the wisdom manifested in creation!

And how full of humility is the comparison which, placing the most ingenious and the most perfect of the efforts of human skill by the side of one of the simplest of the works of nature, shows us but one or two rude steps of approach to it.

How full, too, is it of profit thus to see God in every thing - to find him working with us, and in us, in the daily occupations of our hands, wherein we do but reproduce, under different and inferior forms, his own wisdom and creative power.

A man may thus hold converse with God as intelligibly in art as in nature, and live with him in the workshop, as he may go forth with him in the fields and upon the hills. And whilst he feels himself in those faculties of thought and action, the exercise of which constitute his physical being, to be in very deed a creature made in the image of God, he will not fail to be reminded that the resemblance once embraced with these the qualities of his moral being.

If we conceive space spreading out its dimensions infinitely, still through all its interminable fields does science show it to us peopled with matter - stars upon stars innumerable - a vista in which suns and systems crowd themselves, and to which imagination affixes no limit. If, in like manner, we conceive space to be infinitely divided - as its dimensions grow before the eye of the mind yet less and less - still does it appear a region peopled with the infinite divisions of matter.

On either side is an abyss - an interminable expanse, through which the creative power of God manifests itself, and an unfathomable minuteness.

It is in this last mentioned region of the in accessible minuteness of matter that the principles of the science treated of in the following pages have their origin. Matter is composed of elements, which are inappreciably and infinitely minute; and yet it is within the infinitely minute spaces which separate these elements that the greater number of the forces known to us have their only sensible action. These, including compressibility, extensibility, elasticity, strength, capillary attraction and adhesion, receive their illustration in the first three chapters of the following work. The fourth takes up the Science of Equilibrium, or Statics; applies in numerous examples the fundamental principles of that science, the parallelogram of forces, and the equality of moments; then passes to the question of stability, and to the conditions of the resistance of a surface; traces the operation of each of the mechanical powers under the influence of friction; and embraces the question of the stability of edifices, piers, walls, arches, and domes.

The fifth chapter enters upon the Science of Dynamics. Numerous familiar illustrations establish the permanence of the force which accompanies motion - show how it may be measured - where in a moving body it may be supposed to be collected - exhibit the important mechanical properties of the centres of spontaneous rotation, percussion, and gyration - the nature of centrifugal force, and the properties of the principal axes of a body's rotation - the accumulation and destruction of motion in a moving body, and the laws of gravitation.

The last chapter of the work opens with a series of illustrations, the object of which is to make intelligible, under its most general form, the principle of virtual velocities, and to protect practical men against the errors into which, in the application of this universal principle of mechanics, they are peculiarly liable to fall: it terminates with various illustrations of those general principles which govern the reception, transmission, and application of power by machinery, the measure of dynamical action, and the numerical efficiencies of different agents - principles which receive their final application in an estimate of the dynamical action on the moving and working points of a steam engine.

The Appendix to the work contains a detailed account of the experiments of Messrs Hodgkinson and Fairbairn upon the mechanical properties of hot and cold blast iron: and an extensive series of tables referred to in the body of the work, and including, 1. Tables of the strength of materials; 2. Tables of the weights of cubic feet of different kinds of materials; 3. Tables of the thrusts of semi-circular arches under various circumstances of loading, and of the positions of their points of rupture; 4. Tables of coefficients of friction, and of limiting angles of resistance, compiled and calculated from the recent experiments of M Morin. The results of these admirable experiments, made at the expense of the French government, are here, for the first time, published in this country.

The author has also to acknowledge his obligations to the "Physique" of M Pouillet, for several valuable illustrations and drawings.

6.1. Note.

Henry Moseley is described on the title page as "Late of St John's College, Cambridge; Professor of Natural Philosophy and Astronomy in King's College."

6.2. From the Preface.

In the following work, I have proposed to myself to apply the principles of mechanics to the discussion of the most important and obvious of those questions which present themselves in the practice of the engineer and the architect; and I have sought to include in that discussion all the circumstances on which the practical solution of such questions may be assumed to depend. It includes the substance of a course of lectures delivered to the students of King's College in the department of engineering and architecture, during the years 1840, 1841, 1842. [The first 170 pages of the work were printed for the use of my pupils in the year 1840. Copies of them were about the same time in the possession of several of my friends in the Universities.]

In the first part I have treated of those portions of the science of Statics which have their application in the theory of machines and the theory of construction.

In the second, of the science of Dynamics, and, under this head, particularly of that union of a continued pressure with a continued motion which has received from English writers the various names of "dynamical effect," "efficiency," "work done," "labouring force," "work," &c.; and "moment d'activité," "quantité d'action," "puissance mécanique," "travail," from French writers.

Among the latter this variety of terms has at length given place to the most intelligible and the simplest of them, "travail." The English word "work" is the obvious translation of "travail," and the use of it appears to be recommended by the same considerations. The work of overcoming a pressure of one pound through a space of one foot has in this country been taken as the unit, in terms of which any other amount of work is estimated; and in France the work of overcoming a pressure of one kilogramme through a space of one metre. M Dupin has proposed the application of the term dyname to this unit.

I have gladly sheltered myself from the charge of having contributed to increase the vocabulary of scientific words by assuming the obvious term "unit of work" to represent concisely and conveniently enough the idea which is attached to it, without translation.

The work of any pressure operating through any space is evidently measured in terms of such units, by multiplying the number of pounds in the pressure by the number of feet in the space, if the direction of the pressure be continually that in which the space is described. If not, it follows, by a simple geometrical deduction, that it is measured by the product of the number of pounds in the pressure, by the number of feet in the projection of the space described, upon the direction of the pressure; that is, by the product of the pressure by its virtual velocity. [If the direction of the pressure remain always parallel to itself, the space described may be any finite space; if it do not, the space is understood to be so small, that the direction of the pressure may be supposed to remain parallel to itself whilst that space is described.]

Thus, then, we conclude, at once, by the principle of virtual velocities, that if a machine work under a constant equilibrium of the pressures applied to it, or if it work uniformly, then is the aggregate work of those pressures which tend to accelerate its motion equal to the aggregate work of those which tend to retard it; and, by the principle of vis viva, that if the machine do not work under an equilibrium of the forces impressed upon it, then is the aggregate work of those which tend to accelerate the motion of the machine greater or less than the aggregate work of those which tend to retard its motion by one half the aggregate of the vires vivae acquired or lost by the moving parts of the system, whilst the work is being done upon it. In no respect have the labours of the illustrious president of the Academy of Sciences more contributed to the development of the theory of machines than in the application which he has so successfully made to it of this principle of vis viva. [See Poncelet, Mécanique Industrielle, troisième partie.]

In the elementary discussion of this principle, which is given by M Poncelet, in the introduction to his Mécanique Industrielle, he has revived the term vis inertiae (vis inertiae, vis insita, Newton), and, associating with it the definitive idea of a force of resistance opposed to the acceleration or the retardation of a body's motion, he has shown (Arts. 66. and 122.) the work expended in overcoming this resistance through any space to be measured by one half the vis viva accumulated through the space; so that throwing into the consideration of the forces under which a machine works, the vires inertiae of its moving elements, and observing that one half of their aggregate vis viva is equal to the aggregate work of their vires inertiae, it follows, by the principle of virtual velocities, that the difference be tween the aggregate work of those forces impressed upon a machine, which tend to accelerate its motion, and the aggregate work of those which tend to retard the motion, is equal to the aggregate work of the vires inertiae of the moving parts of the machine: under which form the principle of vis viva resolves itself into the principle of virtual velocities.

So many difficulties, however, oppose themselves to the intro duction of the term vis inertiae, associated with the definitive idea of an opposing force, into the discussion of questions of mechanics, and especially of practical and elementary mechanics, that it has appeared to the author of this work desirable to avoid it. It is with this view, that in the following work a new interpretation is given to that function of the velocity of a moving body which is known as its vis viva; one half that function being interpreted to represent the number of units of work accumulated in the body so long as its motion is continued, and which number of units of work it is capable of reproducing upon any resistance which may be opposed to its motion, and bring it to rest. A very simple investigation (Art. 66.) establishes the truth of this interpretation, and gives to the principle of vis viva the following new and more simple enunciation: - "The difference between the aggregate work done upon the machine, during any time, by those forces which tend to accelerate the motion, and the aggregate work, during the same time, of those which tend to retard the motion, is equal to the aggregate number of units of work accumulated in the moving parts of the machine during that time if the former aggregate exceed the latter, and lost from them during that time if the former aggregate fall short of the latter." Thus, then, if the aggregate work of the forces which tend to accelerate the motion of a machine exceeds that of the forces which tend to retard it, then is the surplus work (that done upon the driving points, above that expended upon the prejudicial resistances and upon the working points) continually accumulated in the moving elements of the machine, and their motion is thereby continually accelerated. And if the former aggregate be less than the latter, then is the deficiency supplied from the work already accumulated in the moving elements, so that their motion is in this case continually retarded.

The moving power divides itself whilst it operates in a machine, first, into that which overcomes the prejudicial resistances of the machine, or those which are opposed by friction and other causes, uselessly absorbing the work in its transmission. Secondly, into that which accelerates the motion of the various moving parts of the machine, and which accumulates in them so long as the work done by the moving power upon it exceeds that expended upon the various resistances opposed to the motion of the machine. Thirdly, into that which overcomes the useful resistances, or those which are opposed to the motion of the machine at the working point, or points, by the useful work which is done by it.

Between these three elements there obtains in every machine a mathematical relation, which I have called its Modulus. The general form of this modulus I have discussed in a memoir on the "Theory of Machines" published in the Philosophical Transactions for the year 1841. The determination of the particular moduli of those elements of machinery which are most commonly in use is the subject of the third part of the following work. From a combination of the moduli of any such elements there results at once the modulus of the machine compounded of them.

When a machine has acquired a state of uniform motion work ceases to accumulate in its moving elements, and its modulus assumes the form of a direct relation between the work done by the motive power upon its driving point and that yielded at its working points. I have determined by a general method* the modulus in this case, from that statical relation between the driving and working pressures upon the machine which obtains in the state bordering upon its motion, and which may be deduced from the known conditions of equilibrium and the established laws of friction. [Art. 152. See Phil. Trans., 1841, p. 290.]

In making this deduction I have, in every case, availed myself of the following principle, first published in my paper on the theory of the arch read before the Cambridge Philosophical Society in Dec.1833, and printed in their Transactions of the following year: - "In the state bordering upon motion of one body upon the surface of another, the resultant pressure upon their common surface of con tact is inclined to the normal, at an angle whose tangent is equal to the coefficient of friction."

This angle I have called the limiting angle of resistance. Its values calculated, in respect to a great variety of surfaces of contact, are given in a table at the conclusion of the second part, from the admirable experiments of M Morin*, in to the mechanical details of which precautions have been introduced hitherto unknown to experiments of this class, and which have given to our knowledge of the laws of friction a precision and a certainty hitherto unhoped for. [See: Nourelles Expériences sur le Frottement, Paris, 1833.]

Of the various elements of machinery those which rotate about cylindrical axes are of the most frequent occurrence and the most useful application; I have, therefore, in the first place sought to establish the general relation of the state bordering upon motion between the driving and the working pressures upon such a machine, reference being had to the weight of the machine. [In my memoir on the "Theory of Machines" (Phil. Trans. 1841), I have extended this relation to the case in which the number of the pressures and their directions are any whatever. The theorem which expresses it is given in the Appendix of this work.]

This relation points out the existence of a particular direction in which the driving pressure should be applied to any such machine, that the amount of work expended upon the friction of the axis may be the least possible. This direction of the driving pressure always presents itself on the same side of the axis with that of the working pressure, and when the latter is vertical it becomes parallel to it; a principle of the economy of power in machinery which has received its application in the parallel motion of the marine engines known as the Gorgon Engines.

I have devoted a considerable space in this portion of my work to the determination of the modulus of a system of toothed wheels; this determination I have, moreover, extended to bevil wheels, and have included in it, with the influence of the friction of the teeth the wheels, that of their axes and their weights. An approximate form of this modulus applies to any shape of the teeth under which they may be made to work correctly; and when in this approximate form of the modulus the terms which represent the influence of the friction of the axis and the weight of the wheel are neglected, it resolves itself into a well known theorem of M Poncelet, reproduced by M Navier and the Rev Dr Whewell. [In the discussion of the friction of the teeth of wheels, the direction of the mutual pressures of the teeth is determined by a method first applied by me to that purpose in a popular treatise, entitled Mechanics applied to the Arts, published in 1834.]

In respect to wheels having epicycloidal and involute teeth, the modulus assumes a character of mathematical exactitude and precision, and at once establishes the conclusion( so often disputed) that the loss of power is greater before the teeth pass the line of centres than at corresponding points afterwards; that the contact should, nevertheless, in all cases take place partly before and partly after the line of centres has been passed. In the case of involute teeth, the pro portion in which the arc of contact should thus be divided by the line of centres is determined by a simple formula; as also are the best dimensions of the base of the involute, with a view to the most perfect economy of power in the working of the wheels.

The greater portion of the subjects discussed in the third part of my work I believe to be entirely new to science. In the fourth part I have treated of "the theory of the stability of structures," referring its conditions, so far as they are dependent upon rotation, to the properties of a certain line which may be conceived to traverse every structure, passing through those points in it where its surfaces of con tact are intersected by the resultant pressures upon them. To this line, whose properties I first dis cussed in a memoir upon "the Stability of a System of Bodies in Contact," printed in the sixth volume of the Camb. Phil. Trans., I have given the name of the line of resistance; it differs essentially in its properties from a line referred to by preceding writers under the name of the curve of equilibrium or the line of pressure. The distance of the line of resistance from the extrados of a structure, at the point where it most nearly approaches it, I have taken as a measure of the stability of a structure, and have called it the modulus of stability; conceiving this measure of the stability to be of more obvious and easier application than the coefficient of stability used by the French writers. [This idea was suggested to me by a rule for the stability of revêtement walls attributed to Vauban, to the effect, that the resultant pressure should intersect the base of such a wall at a point whose distance from its extrados is 4/9ths the distance between the extrados at the base and the vertical through the centre of gravity.]

That structure in respect to every independent element of which, the modulus of stability is the same, is evidently the structure of the greatest stability having a given quantity of material employed in its construction; or of the greatest economy of material having a given stability.

The application of these principles of construction to the theory of piers, walls supported by counter forts and shores, buttresses, walls supporting the thrust of roofs and the weights of the floors of dwellings, and Gothic structures, has suggested to me a class of problems never, I believe, before treated mathematically.

I have applied the well known principle of Coulomb to the determination of the pressure of earth upon revêtement walls, and a modification of that principle, suggested by M Poncelet, to the determination of the resistance opposed to the overthrow of a wall backed by earth. This determination has an obvious application to the theory of foundations.

In the application of the principle of Coulomb I have availed myself, with great advantage, of the properties of the limiting angle of resistance. All my results have thus received a new and a simplified form.

The theory of the arch I have discussed upon principles first laid down in my memoir on "the Theory of the Stability of a System of Bodies in Contact," before referred to, and subsequently in a memoir printed in the " Treatise on Bridges " by Professor Hosking and Mr Hann. [I have made extensive use of the memoir above referred to in the following work, by the obliging permission of the publisher, Mr Weale.]

They differ essentially from those on which the theory of Coulomb is founded; when, nevertheless, applied to the case treated by the French mathematicians they lead to identical results. [The theory of Coulomb was unknown to me at the time of the publication of my memoirs printed in the Camb. Phil. Trans. For a comparison of the two methods see Mr Hann's treatise.]

I have inserted at the conclusion of my work the tables of the thrust of circular arches, calculated by M Garidel from formulae founded on the theory of Coulomb.

The fifth part of the work treats of the "strength of materials," and applies a new method to the de termination of the deflexion of abeam under given pressures.

In the case of a beam loaded uniformly over its whole length, and supported at four different points, I have determined the several pressures upon the points of support by a method applied by M Navier to a similar determination in respect to abeam loaded at given points.

In treating of rupture by elongation I have been led to a discussion of the theory of the suspension bridge. This question, so complicated when reference is had to the weight of the roadway and the weights of the suspending rods, and when the suspending chains are assumed to be of uniform thickness, be comes comparatively easy when the section of the chain is assumed so to vary its dimensions as to be every where of the same strength. A suspension bridge thus constructed is obviously that which, being of a given strength, can be constructed with the least quantity of materials; or, which is of the greatest strength having a given quantity of materials used in its construction. [That particular case of this problem, in which the weights of the suspending rods are neglected, has been treated by Mr Hodgkinson in the fourth vol. of the Manchester Transactions, with his usual ability. He has not, however, succeeded in effecting its complete solution.]

The theory of rupture by transverse strain has suggested a new class of problems, having reference to the forms of girders having wide flanges connected by slender ribs or by open frame work: the consideration of their strongest forms leads to results of practical importance.

In discussing the conditions of the strength of breast-summers, my attention has been directed to the best positions of the columns destined to support them, and to a comparison of the strength of a beam carrying a uniform load and supported freely at its extremities, with that of a beam similarly loaded but having its extremities firmly imbedded in masonry.

In treating of the strength of columns I have gladly replaced the mathematical speculations upon this subject, which are so obviously founded upon false data, by the invaluable experimental results of Mr. E. Hodgkinson, detailed in his well known paper in the Philosophical Transactions for 1840.

The sixth and last part of my work treats on "impact;" and the Appendix includes, together with tables of the mechanical properties of the materials of construction, the angles of rupture and the thrusts of arches, and complete elliptic functions, a demonstration of the admirable theorem of M Poncelet for determining an approximate value of the square root of the sum or difference of two squares.

In respect to the following articles of my work I have to acknowledge my obligations to the work of M Poncelet, entitled Mécanique Industrielle. The mode of demonstration is in some, perhaps, so far varied as that their origin might with difficulty be traced; the principle, however, of each demonstration - all that constitutes its novelty or its value - belongs to that distinguished author.

30 [The enunciation only of this theorem is given in the Méc. Ind., 2me partie, Art.38.],

38, 40, 45, 46, 47, 52, 58, 62, 75,

108 [Some important elements of the demonstration of this theorem are taken from the Méc. Ind., Art. 79. 2me partie. The principle of the demonstration is not, however, the same as in that work.],

123, 202,

267 [In this and the three following articles I have developed the theory of the fly -wheel, under a different form from that adopted by M Poncelet (Méc. Ind., Art.56. 3me partie). The principle of the whole calculation is, however, taken from his work. It probably constitutes one of the most valuable of his contributions to practical science.],

268, 269, 270, 349, 354,

365. [The idea of determining the work necessary to produce a given deflection of abeam from that expended upon the compression and the elongation of its component fibres was suggested by an observation in the Méc. Ind., Art. 75.3me partie. An error presents itself in the determination given by M Poncelet in that article of the linear deflection f of a beam under a given deflecting pressure P. It consists in assuming that the work of the deflecting pressure is represented by Pf, as it would be if, in order to deflect the beam, P must always retain the same value instead of varying directly as the deflection. The true value of the work is 1/2 Pf; the determination of which requires a knowledge of the law of the deflection, which the demonstration does not suppose. It is due to M Poncelet to state that the Mécanique Industrielle was published (uncorrected) without his concurrence or knowledge, in Belgium, from a MS. copy of his lectures lithographed for the use of the workmen at Metz to whom they were addressed.].

6.3. Comments by: T M Charlton.
Notes and Records of the Royal Society of London 30 (2) (1976), 169-179.

The association of Moseley ... with the great railway engineers serves to show that, contrary to popular belief, leading bridge constructors relied heavily upon the scientific method as long ago as the early years of the nineteenth century. It also serves to show that the relevant scientific knowledge had reached a surprisingly advanced stage, even by modern standards: it has been a common fallacy in engineering circles that such knowledge became available only toward the end of that century.
...
Moseley embarked upon a rigorous investigation of the statics of masonry arches and published his findings in 1833, On the equilibrium of the arch, and On a new principle in statics, called the principle of least pressures ...

There seems little doubt that Moseley's major contribution to bridge construction related to the development of the wrought iron girder bridge. The appearance of his excellent book could hardly have been more timely: it was only a few years later that Robert Stephenson, I K Brunel and others with the cooperation of William Fairbairn, were to embark upon some spectacular railway bridge projects taking advantage of the merits of the then novel rolled iron plate and bars. The tubular or hollow iron girder, forerunner of the currently fashionable box girder, was one result.

The particular relevance of Moseley's book to bridge-building lay in its account, with improvements, of Navier's work relating especially to the elastic theory of bending and strength of beams including the effects of bending restraint at terminal supports and continuity over intermediate supports. Those effects which were correctly regarded by leading engineers as conducive to economy or additional strength, are not amenable to analysis by the principles of statics alone. Equations of elasticity relating, for example, to specified conditions of flexure (slope) at supports or to continuity (compatibility of slope) at intermediate supports, are necessary also to provide sufficient equations to enable forces and bending couples to be determined. Moseley's account of the theory was correct by modern standards and it is noteworthy that his pictorial illustrations referred to timber beams, probably because of the early origin through timber-work, of the particular kind of problem. In addition he gave details of experiments carried-out for him by his laboratory assistant, Mr Hatcher, to verify some of the results obtained theoretically.
...
Another important feature of Moseley's book relates to the use of energy as a device in structural mechanics ...

6.4. Comments by: P G Lowe.
Engineering and Education, in Horace R Drew and Sergio Pellegrino (eds.), New Approaches to Structural Mechanics, Shells and Biological Structures (Springer Science & Business Media, 2013), 165-174.

[Henry Moseley] wrote several textbooks, the most important being The Mechanical Principles of Engineering and Architecture, published in 1843. This is a substantial work based on wide reading and investigation by the author. Unlike most other English texts on structural mechanics of the day, Moseley's book discusses the latest European knowledge, especially of the French academic engineers who led the world at the time. The book was also adopted as a text by the US Military Academy at West Point, and can be assumed to have exerted some influence on their methods and outlook. The Great Exhibition of 1851 contributed to the realisation that American industry was becoming competitive with British and European industry. Moseley produced a revised and enlarged edition of his book in 1855. The Great Exhibition profits, which were very substantial, were largely ear-marked for promotion of education and particularly technical education, with the strong support of Albert. the Prince Consort. Towards the end of the century the main fruits were to be seen as the Imperial College and the nearby Museums. Clerk Maxwell, who was a later occupant of the Kings College London Chair, is recorded by his biographers as having studied Moseley's The Mechanical Principles of Engineering and Architecture while preparing for the Tripos in the early 1850's.