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diff --git a/old/69053-0.txt b/old/69053-0.txt deleted file mode 100644 index bdee2c9..0000000 --- a/old/69053-0.txt +++ /dev/null @@ -1,6810 +0,0 @@ -The Project Gutenberg eBook of The conservation of energy, by Balfour -Stewart - -This eBook is for the use of anyone anywhere in the United States and -most other parts of the world at no cost and with almost no restrictions -whatsoever. You may copy it, give it away or re-use it under the terms -of the Project Gutenberg License included with this eBook or online at -www.gutenberg.org. If you are not located in the United States, you -will have to check the laws of the country where you are located before -using this eBook. - -Title: The conservation of energy - -Author: Balfour Stewart - -Release Date: September 27, 2022 [eBook #69053] - -Language: English - -Produced by: Nina Akalis 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 THE CONSERVATION OF -ENERGY *** - - - - - - THE INTERNATIONAL SCIENTIFIC SERIES. - - VOLUME VII. - - - - -THE INTERNATIONAL SCIENTIFIC SERIES. - -_Works already Published._ - - - I. FORMS OF WATER, IN CLOUDS, RAIN, RIVERS, ICE, AND GLACIERS. By - Prof. JOHN TYNDALL, LL. D., F. R. S. 1 vol. Cloth. Price, $1.50. - - II. PHYSICS AND POLITICS; OR, THOUGHTS ON THE APPLICATION OF - THE PRINCIPLES OF “NATURAL SELECTION” AND “INHERITANCE” TO - POLITICAL SOCIETY. By WALTER BAGEHOT, Esq., author of “The English - Constitution.” 1 vol. Cloth. Price, $1.50. - - III. FOODS. By EDWARD SMITH, M. D., LL. B., F. R. S. 1 vol. Cloth. - Price, $1.75. - - IV. MIND AND BODY: THE THEORIES OF THEIR RELATIONS. By ALEX. BAIN, LL. - D., Professor of Logic in the University of Aberdeen, 1 vol., 12mo. - Cloth. Price, $1.50. - - V. THE STUDY OF SOCIOLOGY. By HERBERT SPENCER. Price, $1.50. - - VI. THE NEW CHEMISTRY. By Prof. JOSIAH P. COOKE, Jr., of Harvard - University. 1 vol., 12mo. Cloth. Price, $2.00. - - VII. THE CONSERVATION OF ENERGY. By Prof. BALFOUR STEWART, LL. D., F. - R. S. 1 vol., 12mo. Cloth. Price, $1.50. - - VIII. ANIMAL LOCOMOTION; OR, WALKING, SWIMMING, AND FLYING, WITH A - DISSERTATION ON AËRONAUTICS. By J. BELL PETTIGREW, M. D., F. R. S. E., - F. R. C. P. E. 1 vol., 12mo. Fully illustrated. Price, $1.75. - - IX. RESPONSIBILITY IN MENTAL DISEASE. By HENRY MAUDSLEY, M. D. 1 vol., - 12mo. Cloth. Price, $1.50. - - X. THE SCIENCE OF LAW. By Prof. SHELDON AMOS. 1 vol., 12mo. Cloth. - Price, $1.75. - - XI. ANIMAL MECHANISM. A TREATISE ON TERRESTRIAL AND AËRIAL LOCOMOTION. - By E. J. MAREY. With 117 Illustrations. Price, $1.75. - - XII. THE HISTORY OF THE CONFLICT BETWEEN RELIGION AND SCIENCE. By JOHN - WM. DRAPER, M. D., LL. D., author of “The Intellectual Development of - Europe.” Price, $1.75. - - XIII. THE DOCTRINE OF DESCENT, AND DARWINISM. By Prof. OSCAR SCHMIDT, - Strasburg University. Price, $1.50. - - XIV. THE CHEMISTRY OF LIGHT AND PHOTOGRAPHY. IN ITS APPLICATION TO - ART, SCIENCE, AND INDUSTRY. By Dr. HERMANN VOGEL. 100 Illustrations. - Price, $2.00. - - XV. FUNGI; THEIR NATURE, INFLUENCE, AND USES. By M. C. COOKE, M. - A., LL. D. Edited by Rev. M. J. BERKELEY, M. A., F. L. S. With 109 - Illustrations. Price, $1.50. - - XVI. THE LIFE AND GROWTH OF LANGUAGE. By Prof. W. D. WHITNEY, of Yale - College. Price, $1.50. - - XVII. THE NATURE OF LIGHT, WITH A GENERAL ACCOUNT OF PHYSICAL - OPTICS. By Dr. EUGENE LOMMEL, Professor of Physics in the University - of Erlangen. With 188 Illustrations and a Plate of Spectra in - Chromo-lithography. (_In press._) - - - - - THE INTERNATIONAL SCIENTIFIC SERIES. - - THE - - CONSERVATION OF ENERGY. - - BY - - BALFOUR STEWART, LL. D., F.R.S., - PROFESSOR OF NATURAL PHILOSOPHY AT THE OWENS COLLEGE, MANCHESTER. - - - _WITH AN APPENDIX_, - - TREATING OF THE VITAL AND MENTAL APPLICATIONS OF THE - DOCTRINE - - - NEW YORK: - D. APPLETON AND COMPANY, - 549 & 551 BROADWAY. - 1875. - - - - - ENTERED, according to Act of Congress, in the year 1874, by - D. APPLETON & COMPANY, - In the Office of the Librarian of Congress, at Washington. - - - - -NOTE TO THE AMERICAN EDITION. - - -The great prominence which the modern doctrine of the Conservation of -Energy or Correlation of Forces has lately assumed in the world of -thought, has made a simple and popular explanation of the subject very -desirable. The present work of Dr. Balfour Stewart, contributed to the -International Scientific Series, fully meets this requirement, as it -is probably the clearest and most elementary statement of the question -that has yet been attempted. Simple in language, copious and familiar -in illustration, and remarkably lucid in the presentation of facts and -principles, his little treatise forms just the introduction to the -great problem of the interaction of natural forces that is required by -general readers. But Professor Stewart having confined himself mainly -to the physical aspects of the subject, it was desirable that his views -should be supplemented by a statement of the operation of the principle -in the spheres of life and mind. An Appendix has, accordingly, been -added to the American edition of Dr. Stewart’s work, in which these -applications of the law are considered. - -Professor Joseph Le Conte published a very able essay fourteen years -ago on the Correlation of the Physical and Vital Forces, which was -extensively reprinted abroad, and placed the name of the author among -the leading interpreters of the subject. His mode of presenting it was -regarded as peculiarly happy, and was widely adopted by other writers. -After further investigations and more mature reflection, he has -recently restated his views, and has kindly furnished the revised essay -for insertion in this volume. - -Professor A. Bain, the celebrated Psychologist of Aberdeen, who -has done so much to advance the study of mind in its physiological -relations, prepared an interesting lecture not long ago on the -“Correlation of the Nervous and Mental Forces,” which was read with -much interest at the time of its publication, and is now reprinted as a -suitable exposition of that branch of the subject. These two essays, by -carrying out the principle in the field of vital and mental phenomena, -will serve to give completeness and much greater value to the present -volume. - - NEW YORK, _December, 1873_. - - - - -PREFACE. - - -We may regard the Universe in the light of a vast physical machine, and -our knowledge of it may be conveniently divided into two branches. - -The one of these embraces what we know regarding the structure of the -machine itself, and the other what we know regarding its method of -working. - -It has appeared to the author that, in a treatise like this, these two -branches of knowledge ought as much as possible to be studied together, -and he has therefore endeavored to adopt this course in the following -pages. He has regarded a universe composed of atoms with some sort of -medium between them as the machine, and the laws of energy as the laws -of working of this machine. - -The first chapter embraces what we know regarding atoms, and gives -also a definition of Energy. The various forces and energies of Nature -are thereafter enumerated, and the law of Conservation is stated. Then -follow the various transmutations of Energy, according to a list, for -which the author is indebted to Prof. Tait. The fifth chapter gives -a short historical sketch of the subject, ending with the law of -Dissipation; while the sixth and last chapter gives some account of the -position of living beings in this universe of Energy. - - B. S. - - _The Owens College, Manchester, - August, 1873._ - - - - -CONTENTS. - - - NOTE TO THE AMERICAN EDITION, v - - PREFACE, vii - - - CHAPTER - - I.--WHAT IS ENERGY? 1 - - II.--MECHANICAL ENERGY AND ITS CHANGE INTO HEAT, 23 - - III.--THE FORCES AND ENERGIES OF NATURE: THE LAW OF CONSERVATION, 48 - - IV.--TRANSMUTATIONS OF ENERGY, 87 - - V.--HISTORICAL SKETCH: THE DISSIPATION OF ENERGY, 131 - - VI.--THE POSITION OF LIFE, 154 - - - APPENDIX - - I.--CORRELATION OF VITAL WITH CHEMICAL AND PHYSICAL FORCES. - By JOSEPH LE CONTE, Professor of Geology and Natural - History in the University of California, 171 - - II.--CORRELATION OF NERVOUS AND MENTAL FORCES. By ALEXANDER - BAIN, Professor of Logic and Mental Philosophy in - the University of Aberdeen, 205 - - - - -THE CONSERVATION OF ENERGY. - - - - -CHAPTER I. - -_WHAT IS ENERGY?_ - - -_Our Ignorance of Individuals._ - -1. Very often we know little or nothing of individuals, while we yet -possess a definite knowledge of the laws which regulate communities. - -The Registrar-General, for example, will tell us that the death-rate -in London varies with the temperature in such a manner that a very -low temperature is invariably accompanied by a very high death-rate. -But if we ask him to select some one individual, and explain to us in -what manner his death was caused by the low temperature, he will, most -probably, be unable to do so. - -Again, we may be quite sure that after a bad harvest there will be a -large importation of wheat into the country, while, at the same time, -we are quite ignorant of the individual journeys of the various -particles of flour that go to make up a loaf of bread. - -Or yet again, we know that there is a constant carriage of air from the -poles to the equator, as shown by the trade winds, and yet no man is -able to individualize a particle of this air, and describe its various -motions. - -2. Nor is our knowledge of individuals greater in the domains of -physical science. We know nothing, or next to nothing, of the ultimate -structure and properties of matter, whether organic or inorganic. - -No doubt there are certain cases where a large number of particles -are linked together, so as to act as one individual, and then we can -predict its action--as, for instance, in the solar system, where the -physical astronomer is able to foretell with great exactness the -positions of the various planets, or of the moon. And so, in human -affairs, we find a large number of individuals acting together as one -nation, and the sagacious statesman taking very much the place of the -sagacious astronomer, with regard to the action and reaction of various -nations upon one another. - -But if we ask the astronomer or the statesman to select an individual -particle and an individual human being, and predict the motions of -each, we shall find that both will be completely at fault. - -3. Nor have we far to look for the cause of their ignorance. A -continuous and restless, nay, a very complicated, activity is the order -of nature throughout all her individuals, whether these be living -beings or inanimate particles of matter. Existence is, in truth, one -continued fight, and a great battle is always and everywhere raging, -although the field in which it is fought is often completely shrouded -from our view. - -4. Nevertheless, although we cannot trace the motions of individuals, -we may sometimes tell the result of the fight, and even predict how the -day will go, as well as specify the causes that contribute to bring -about the issue. - -With great freedom of action and much complication of motion in the -individual, there are yet comparatively simple laws regulating the -joint result attainable by the community. - -But, before proceeding to these, it may not be out of place to take a -very brief survey of the organic and inorganic worlds, in order that -our readers, as well as ourselves, may realize our common ignorance of -the ultimate structure and properties of matter. - -5. Let us begin by referring to the causes which bring about disease. -It is only very recently that we have begun to suspect a large number -of our diseases to be caused by organic germs. Now, assuming that we -are right in this, it must nevertheless be confessed that our ignorance -about these germs is most complete. It is perhaps doubtful whether we -ever saw one of these organisms,[1] while it is certain that we are in -profound ignorance of their properties and habits. - -We are told by some writers[2] that the very air we breathe is -absolutely teeming with germs, and that we are surrounded on all sides -by an innumerable array of minute organic beings. It has also been -conjectured that they are at incessant warfare among themselves, and -that we form the spoil of the stronger party. Be this as it may, we -are at any rate intimately bound up with, and, so to speak, at the -mercy of, a world of creatures, of which we know as little as of the -inhabitants of the planet Mars. - -6. Yet, even here, with profound ignorance of the individual, we are -not altogether unacquainted with some of the habits of these powerful -predatory communities. Thus we know that cholera is eminently a low -level disease, and that during its ravages we ought to pay particular -attention to the water we drink. This is a general law of cholera, -which is of the more importance to us because we cannot study the -habits of the individual organisms that cause the disease. - -Could we but see these, and experiment upon them, we should soon -acquire a much more extensive knowledge of their habits, and perhaps -find out the means of extirpating the disease, and of preventing its -recurrence. - -Again, we know (thanks to Jenner) that vaccination will prevent the -ravages of small-pox, but in this instance we are no better off than -a band of captives who have found out in what manner to mutilate -themselves, so as to render them uninteresting to their victorious foe. - -7. But if our knowledge of the nature and habits of organized molecules -be so small, our knowledge of the ultimate molecules of inorganic -matter is, if possible, still smaller. It is only very recently that -the leading men of science have come to consider their very existence -as a settled point. - -In order to realize what is meant by an inorganic molecule, let us -take some sand and grind it into smaller and smaller particles, and -these again into still smaller. In point of fact we shall never -reach the superlative degree of smallness by this operation--yet in -our imagination we may suppose the sub-division to be carried on -continuously, always making the particles smaller and smaller. In -this case we should, at last, come to an ultimate molecule of sand or -oxide of silicon, or, in other words, we should arrive at the smallest -entity retaining all the properties of sand, so that were it possible -to divide the molecule further the only result would be to separate it -into its chemical constituents, consisting of silicon on the one side -and oxygen on the other. - -We have, in truth, much reason to believe that sand, or any other -substance, is incapable of infinite sub-division, and that all we can -do in grinding down a solid lump of anything is to reduce it into lumps -similar to the original, but only less in size, each of these small -lumps containing probably a great number of individual molecules. - -8. Now, a drop of water no less than a grain of sand is built up of a -very great number of molecules, attached to one another by the force of -cohesion--a force which is much stronger in the sand than in the water, -but which nevertheless exists in both. And, moreover, Sir William -Thomson, the distinguished physicist, has recently arrived at the -following conclusion with regard to the size of the molecules of water. -He imagines a single drop of water to be magnified until it becomes -as large as the earth, having a diameter of 8000 miles, and all the -molecules to be magnified in the same proportion; and he then concludes -that a single molecule will appear, under these circumstances, as -somewhat larger than a shot, and somewhat smaller than a cricket ball. - -9. Whatever be the value of this conclusion, it enables us to realize -the exceedingly small size of the individual molecules of matter, -and renders it quite certain that we shall never, by means of the -most powerful microscope, succeed in making visible these ultimate -molecules. For our knowledge of the sizes, shapes, and properties -of such bodies, we must always, therefore, be indebted to indirect -evidence of a very complicated nature. - -It thus appears that we know little or nothing about the shape or size -of molecules, or about the forces which actuate them; and, moreover, -the very largest masses of the universe share with the very smallest -this property of being beyond the direct scrutiny of the human -senses--the one set because they are so far away, and the other because -they are so small. - -10. Again, these molecules are not at rest, but, on the contrary, they -display an intense and ceaseless energy in their motions. There is, -indeed, an uninterrupted warfare going on--a constant clashing together -of these minute bodies, which are continually maimed, and yet always -recover themselves, until, perhaps, some blow is struck sufficiently -powerful to dissever the two or more simple atoms that go to form a -compound molecule. A new state of things thenceforward is the result. - -But a simple elementary atom is truly an immortal being, and enjoys the -privilege of remaining unaltered and essentially unaffected amid the -most powerful blows that can be dealt against it--it is probably in a -state of ceaseless activity and change of form, but it is nevertheless -always the same. - -11. Now, a little reflection will convince us that we have in this -ceaseless activity another barrier to an intimate acquaintance with -molecules and atoms, for even if we could see them they would not -remain at rest sufficiently long to enable us to scrutinize them. - -No doubt there are devices by means of which we can render visible, for -instance, the pattern of a quickly revolving coloured disc, for we may -illuminate it by a flash of electricity, and the disc may be supposed -to be stationary during the extremely short time of the flash. But we -cannot say the same about molecules and atoms, for, could we see an -atom, and could we illuminate it by a flash of electricity, the atom -would most probably have vibrated many times during the exceedingly -small time of the flash. In fine, the limits placed upon our senses, -with respect to space and time, equally preclude the possibility of our -ever becoming directly acquainted with these exceedingly minute bodies, -which are nevertheless the raw materials of which the whole universe is -built. - - -_Action and Reaction, Equal and Opposite._ - -12. But while an impenetrable veil is drawn over the individual in this -warfare of clashing atoms, yet we are not left in profound ignorance -of the laws which determine the ultimate result of all these motions, -taken together as a whole. - - -_In a Vessel of Goldfish._ - -Let us suppose, for instance, that we have a glass globe containing -numerous goldfish standing on the table, and delicately poised on -wheels, so that the slightest push, the one way or the other, would -make it move. These goldfish are in active and irregular motion, and he -would be a very bold man who should venture to predict the movements of -an individual fish. But of one thing we may be quite certain: we may -rest assured that, notwithstanding all the irregular motions of its -living inhabitants, the globe containing the goldfish will remain at -rest upon its wheels. - -Even if the table were a lake of ice, and the wheels were extremely -delicate, we should find that the globe would remain at rest. Indeed, -we should be exceedingly surprised if we found the globe going away of -its own accord from the one side of the table to the other, or from -the one side of a sheet of ice to the other, in consequence of the -internal motions of its inhabitants. Whatever be the motions of these -individual units, yet we feel sure that the globe cannot move itself -_as a whole_. In such a system, therefore, and, indeed, in every system -left to itself, there may be strong internal forces acting between -the various parts, but these _actions and reactions are equal and -opposite_, so that while the small parts, whether visible or invisible, -are in violent commotion among themselves, yet the system as a whole -will remain at rest. - - -_In a Rifle._ - -13. Now it is quite a legitimate step to pass from this instance of the -goldfish to that of a rifle that has just been fired. In the former -case, we imagined the globe, together with its fishes, to form one -system; and in the latter, we must look upon the rifle, with its powder -and ball, as forming one system also. - -Let us suppose that the explosion takes place through the application -of a spark. Although this spark is an external agent, yet if we reflect -a little we shall see that its only office in this case is to summon -up the internal forces already existing in the loaded rifle, and bring -them into vigorous action, and that in virtue of these internal forces -the explosion takes place. - -The most prominent result of this explosion is the out-rush of the -rifle ball with a velocity that may, perhaps, carry it for the best -part of a mile before it comes to rest; and here it would seem to us, -at first sight, that the law of equal action and reaction is certainly -broken, for these internal forces present in the rifle have at least -propelled part of the system, namely, the rifle ball, with a most -enormous velocity in one direction. - -14. But a little further reflection will bring to light another -phenomenon besides the out-rush of the ball. It is well known to all -sportsmen that when a fowling-piece is discharged, there is a kick or -recoil of the piece itself against the shoulder of the sportsman, which -he would rather get rid of, but which we most gladly welcome as the -solution of our difficulty. In plain terms, while the ball is projected -forwards, the rifle stock (if free to move) is at the same moment -projected backwards. To fix our ideas, let us suppose that the rifle -stock weighs 100 ounces, and the ball one ounce, and that the ball is -projected forwards with the velocity of 1000 feet per second; then it -is asserted, by the law of action and reaction, that the rifle stock is -at the same time projected backwards with the velocity of 10 feet per -second, so that the mass of the stock, multiplied by its velocity of -recoil, shall precisely equal the mass of the ball, multiplied by its -velocity of projection. The one product forms a measure of the action -in the one direction, and the other of the reaction in the opposite -direction, and thus we see that in the case of a rifle, as well as in -that of the globe of fish, action and reaction are equal and opposite. - - -_In a Falling Stone._ - -15. We may even extend the law to cases in which we do not perceive -the recoil or reaction at all. Thus, if I drop a stone from the -top of a precipice to the earth, the motion seems all to be in one -direction, while at the same time it is in truth the result of a mutual -attraction between the earth and the stone. Does not the earth move -also? We cannot see it move, but we are entitled to assert that it -does in reality move upwards to meet the stone, although quite to an -imperceptible extent, and that the law of action and reaction holds -here as truly as in a rifle, the only difference being that in the -one case the two objects are rushing together, while in the other -they are rushing apart. Inasmuch, however, as the mass of the earth -is very great compared with that of the stone, it follows that its -velocity must be extremely small, in order that the mass of the earth, -multiplied into its velocity upwards, shall equal the mass of the -stone, multiplied into its velocity downwards. - -16. We have thus, in spite of our ignorance of the ultimate atoms and -molecules of matter, arrived at a general law which regulates the -action of internal forces. We see that these forces are always mutually -exerted, and that if A attracts or repels B, B in its turn attracts or -repels A. We have here, in fact, a very good instance of that kind of -generalization, which we may arrive at, even in spite of our ignorance -of individuals. - -But having now arrived at this law of action and reaction, do we know -all that it is desirable to know? have we got a complete understanding -of what takes place in all such cases--for instance, in that of the -rifle which is just discharged? Let us consider this point a little -further. - - -_The Rifle further considered._ - -17. We define quantity of motion to mean the product of the mass by -the velocity; and since the velocity of recoil of the rifle stock, -multiplied by the mass of the stock, is equal to the velocity of -projection of the rifle ball, multiplied by the mass of the ball, we -conceive ourselves entitled to say that the quantity of motion, or -momentum, generated is equal in both directions, so that the law of -action and reaction holds here also. Nevertheless, it cannot but occur -to us that, _in some sense_, the motion of the rifle ball is a very -different thing from that of the stock, for it is one thing to allow -the stock to recoil against your shoulder and discharge the ball into -the air, and a very different thing to discharge the ball against your -shoulder and allow the stock to fly into the air. And if any man -should assert the absolute equality between the blow of the rifle stock -and that of the rifle ball, you might request him to put his assertion -to this practical test, with the absolute certainty that he would -decline. Equality between the two!--Impossible! Why, if this were the -case, a company of soldiers engaged in war would suffer much more than -the enemy against whom they fired, for the soldiers would certainly -feel each recoil, while the enemy would suffer from only a small -proportion of the bullets. - - -_The Rifle Ball possesses Energy._ - -18. Now, what is the meaning of this great difference between the two? -We have a vivid perception of a mighty difference, and it only remains -for us to clothe our naked impressions in a properly fitting scientific -garb. - -_The something which the rifle ball possesses in contradistinction to -the rifle stock is clearly the power of overcoming resistance._ It -can penetrate through oak wood or through water, or (alas! that it -should be so often tried) through the human body, and this power of -penetration is the distinguishing characteristic of a substance moving -with very great velocity. - -19. Let us define by the term _energy_ this power which the rifle -ball possesses of overcoming obstacles or of doing work. Of course -we use the word work without reference to the moral character of the -thing done, and conceive ourselves entitled to sum up, with perfect -propriety and innocence, the amount of work done in drilling a hole -through a deal board or through a man. - -20. A body such as a rifle ball, moving with very great velocity, -has, therefore, energy, and it requires very little consideration -to perceive that this _energy will be proportional to its weight or -mass_, for a ball of two ounces moving with the velocity of 1000 feet -per second will be the same as two balls of one ounce moving with this -velocity, but the energy of two similarly moving ounce balls will -manifestly be double that of one, so that the energy is proportional -to the weight, if we imagine that, meanwhile, the velocity remains the -same. - -21. But, on the other hand, the energy is not simply proportional to -the velocity, for, if it were, the energy of the rifle stock and of the -rifle ball would be the same, inasmuch as the rifle stock would gain as -much by its superior mass as it would lose by its inferior velocity. -Therefore, the energy of a moving body increases with the velocity more -quickly than a simple proportion, so that if the velocity be doubled, -the energy is more than doubled. Now, in what manner does the energy -increase with the velocity? That is the question we have now to answer, -and, in doing so, we must appeal to the familiar facts of everyday -observation and experience. - -22. In the first place, it is well known to artillerymen, that if -a ball have a double velocity, its penetrating power or energy is -increased nearly fourfold, so that it will pierce through four, or -nearly four, times as many deal boards as the ball with only a single -velocity--in other words, they will tell us in mathematical language, -that the energy varies as the square of the velocity. - - -_Definition of Work._ - -23. And now, before proceeding further, it will be necessary to tell -our readers how to measure work in a strictly scientific manner. We -have defined energy to be the power of doing work, and although every -one has a general notion of what is meant by work, that notion may not -be sufficiently precise for the purpose of this volume. How, then, are -we to measure work? Fortunately, we have not far to go for a practical -means of doing this. Indeed, there is a force at hand which enables us -to accomplish this measurement with the greatest precision, and this -force is gravity. Now, the first operation in any kind of numerical -estimate is to fix upon our unit or standard. Thus we say a rod is -so many inches long, or a road so many miles long. Here an inch and -a mile are chosen as our standards. In like manner, we speak of so -many seconds, or minutes, or hours, or days, or years, choosing that -standard of time or duration which is most convenient for our purpose. -So in like manner we must choose our unit of work, but in order to -do so we must first of all choose our units of weight and of length, -and for these we will take the _kilogramme_ and the _metre_, these -being the units of the metrical system. The kilogramme corresponds -to about 15,432·35 English grains, being rather more than two pounds -avoirdupois, and the metre to about 39·371 English inches. - -Now, if we raise a kilogramme weight one metre in vertical height, -we are conscious of putting forth an effort to do so, and of being -resisted in the act by the force of gravity. In other words, we spend -energy and do work in the process of raising this weight. - -Let us agree to consider the energy spent, or the work done, in this -operation as one unit of work, and let us call it the _kilogrammetre_. - -24. In the next place, it is very obvious that if we raise the -kilogramme two metres in height, we do two units of work--if three -metres, three units, and so on. - -And again, it is equally obvious that if we raise a weight of two -kilogrammes one metre high, we likewise do two units of work, while if -we raise it two metres high, we do four units, and so on. - -From these examples we are entitled to derive the following -rule:--_Multiply the weight raised (in kilogrammes) by the vertical -height (in metres) through which it is raised, and the result will be -the work done (in kilogrammetres)._ - - -_Relation between Velocity and Energy._ - -25. Having thus laid a numerical foundation for our superstructure, -let us next proceed to investigate the relation between velocity and -energy. But first let us say a few words about velocity. This is one -of the few cases in which everyday experience will aid, rather than -hinder, us in our scientific conception. Indeed, we have constantly -before us the example of bodies moving with variable velocities. - -Thus a railway train is approaching a station and is just beginning to -slacken its pace. When we begin to observe, it is moving at the rate of -forty miles an hour. A minute afterwards it is moving at the rate of -twenty miles only, and a minute after that it is at rest. For no two -consecutive moments has this train continued to move at the same rate, -and yet we may say, with perfect propriety, that at such a moment the -train was moving, say, at the rate of thirty miles an hour. We mean, of -course, that had it continued to move for an hour with the speed which -it had when we made the observation, it would have gone over thirty -miles. We know that, as a matter of fact, it did not move for two -seconds at that rate, but this is of no consequence, and hardly at all -interferes with our mental grasp of the problem, so accustomed are we -all to cases of variable velocity. - -26. Let us now imagine a kilogramme weight to be shot vertically -upwards, with a certain initial velocity--let us say, with the velocity -of 9·8 metres in one second. Gravity will, of course, act against the -weight, and continually diminish its upward speed, just as in the -railway train the break was constantly reducing the velocity. But yet -it is very easy to see what is meant by an initial velocity of 9·8 -metres per second; it means that if gravity did not interfere, and if -the air did not resist, and, in fine, if no external influence of any -kind were allowed to act upon the ascending mass, it would be found to -move over 9·8 metres in one second. - -Now, it is well known to those who have studied the laws of motion, -that a body, shot upwards with the velocity of 9·8 metres in one -second, will be brought to rest when it has risen 4·9 metres in height. -If, therefore, it be a kilogramme, its upward velocity will have -enabled it to raise itself 4·9 metres in height against the force of -gravity, or, in other words, it will have done 4·9 units of work; and -we may imagine it, when at the top of its ascent, and just about to -turn, caught in the hand and lodged on the top of a house, instead of -being allowed to fall again to the ground. We are, therefore, entitled -to say that a kilogramme, shot upwards with the velocity of 9·8 metres -per second, has energy equal to 4·9, inasmuch as it can raise itself -4·9 metres in height. - -27. Let us next suppose that the velocity with which the kilogramme -is shot upwards is that of 19·6 metres per second. It is known to all -who have studied dynamics that the kilogramme will now mount not only -twice, but four times as high as it did in the last instance--in other -words, it will now mount 19·6 metres in height. - -Evidently, then, in accordance with our principles of measurement, -the kilogramme has now four times as much energy as it had in the -last instance, because it can raise itself four times as high, and -therefore do four times as much work, and thus we see that the energy -is increased four times by doubling the velocity. - -Had the initial velocity been three times that of the first instance, -or 29·4 metres per second, it might in like manner be shown that the -height attained would have been 44·1 metres, so that by tripling the -velocity the energy is increased nine times. - -28. We thus see that whether we measure the energy of a moving body by -the thickness of the planks through which it can pierce its way, or by -the height to which it can raise itself against gravity, the result -arrived at is the same. _We find the energy to be proportional to the -square of the velocity_, and we may formularize our conclusion as -follows:-- - -Let _v_ = the initial velocity expressed in metres per second, then -the energy in kilogrammetres = _v_²/19·6. Of course, if the body shot -upwards weighs two kilogrammes, then everything is doubled, if three -kilogrammes, tripled, and so on; so that finally, if we denote by -_m_ the mass of the body in kilogrammes, we shall have the energy in -kilogrammetres = _mv_²/19·6. To test the truth of this formula, we have -only to apply it to the cases described in Arts. 26 and 27. - -29. We may further illustrate it by one or two examples. For instance, -let it be required to find the energy contained in a mass of five -kilogrammes, shot upwards with the velocity of 20 metres per second. - -Here we have _m_ = 5 and _v_ = 20, hence-- - - Energy = 5(20)²/(19·6) = 2000/(19·6) = 102·04 nearly. - -Again, let it be required to find the height to which the mass of the -last question will ascend before it stops. We know that its energy is -102·04, and that its mass is 5. Dividing 102·04 by 5, we obtain 20·408 -as the height to which this mass of five kilogrammes must ascend in -order to do work equal to 102·04 kilogrammetres. - -30. In what we have said we have taken no account either of the -resistance or of the buoyancy of the atmosphere; in fact, we have -supposed the experiments to be made in vacuo, or, if not in vacuo, -made by means of a heavy mass, like lead, which will be very little -influenced either by the resistance or buoyancy of the air. - -We must not, however, forget that if a sheet of paper, or a feather, -be shot upwards with the velocities mentioned in our text, they will -certainly not rise in the air to nearly the height recorded, but -will be much sooner brought to a stop by the very great resistance -which they encounter from the air, on account of their great surface, -combined with their small mass. - -On the other hand, if the substance we make use of be a large light bag -filled with hydrogen, it will find its way upwards without any effort -on our part, and we shall certainly be doing no work by carrying it -one or more metres in height--it will, in reality, help to pull us up, -instead of requiring help from us to cause it to ascend. In fine, what -we have said is meant to refer to the force of gravity alone, without -taking into account a resisting medium such as the atmosphere, the -existence of which need not be considered in our present calculations. - -31. It should likewise be remembered, that while the energy of a moving -body depends upon its velocity, it is independent of the direction in -which the body is moving. We have supposed the body to be shot upwards -with a given velocity, but it might be shot horizontally with the same -velocity, when it would have precisely the same energy as before. A -cannon ball, if fired vertically upwards, may either be made to spend -its energy in raising itself, or in piercing through a series of deal -boards. Now, if the same ball be fired horizontally with the same -velocity it will pierce through the same number of deal boards. - -In fine, direction of motion is of no consequence, and the only reason -why we have chosen vertical motion is that, in this case, there is -always the force of gravity steadily and constantly opposing the motion -of the body, and enabling us to obtain an accurate measure of the work -which it does by piercing its way upwards against this force. - -32. But gravity is not the only force, and we might measure the energy -of a moving body by the extent to which it would bend a powerful -spring or resist the attraction of a powerful magnet, or, in fine, -we might make use of the force which best suits our purpose. If this -force be a constant one, we must measure the energy of the moving body -by the space which it is able to traverse against the action of the -force--just as, in the case of gravity, we measured the energy of the -body by the space through which it was able to raise itself against its -own weight. - -33. We must, of course, bear in mind that if this force be more -powerful than gravity, a body moved a short distance against it will -represent the expenditure of as much energy as if it were moved a -greater distance against gravity. In fine, we must take account both of -the strength of the force and of the distance moved over by the body -against it before we can estimate in an accurate matter the work which -has been done. - - -FOOTNOTES: - -[1] It is said that there are one or two instances where the microscope -has enlarged them into visibility. - -[2] _See_ Dr. Angus Smith on Air and Rain. - - - - -CHAPTER II. - -_MECHANICAL ENERGY AND ITS CHANGE INTO HEAT._ - - -_Energy of Position. A Stone high up._ - -34. In the last chapter it was shown what is meant by energy, and how -it depends upon the velocity of a moving body; and now let us state -that this same energy or power of doing work may nevertheless be -possessed by a body absolutely at rest. It will be remembered (Art. -26) that in one case where a kilogramme was shot vertically upwards, -we supposed it to be caught at the summit of its flight and lodged on -the top of a house. Here, then, it rests without motion, but yet not -without the power of doing work, and hence not without energy. For we -know very well that if we let it fall it will strike the ground with -as much velocity, and, therefore, with as much energy, as it had when -it was originally projected upwards. Or we may, if we choose, make use -of its energy to assist us in driving in a pile, or utilize it in a -multitude of ways. - -In its lofty position it is, therefore, not without energy, but this is -of a quiet nature, and not due in the least to motion. To what, then, -is it due? We reply--to the position which the kilogramme occupies at -the top of the house. For just as a body in motion is a very different -thing (as regards energy) from a body at rest, so is a body at the top -of a house a very different thing from a body at the bottom. - -To illustrate this, we may suppose that two men of equal activity and -strength are fighting together, each having his pile of stones with -which he is about to belabour his adversary. One man, however, has -secured for himself and his pile an elevated position on the top of a -house, while his enemy has to remain content with a position at the -bottom. Now, under these circumstances, you can at once tell which of -the two will gain the day--evidently the man on the top of the house, -and yet not on account of his own superior energy, but rather on -account of the energy which he derives from the elevated position of -his pile of stones. We thus see that there is a kind of energy derived -from position, as well as a kind derived from velocity, and we shall, -in future, call the former _energy of position_, and the latter _energy -of motion_. - - -_A Head of Water._ - -35. In order to vary our illustration, let us suppose there are two -mills, one with a large pond of water near it and at a high level, -while the other has also a pond, but at a lower level than itself. We -need hardly ask which of the two is likely to work--clearly the one -with the pond at a low level can derive from it no advantage whatever, -while the other may use the high level pond, or head of water, as -this is sometimes called, to drive its wheel, and do its work. There -is, thus, a great deal of work to be got out of water high up--real -substantial work, such as grinding corn or thrashing it, or turning -wood or sawing it. On the other hand, there is no work at all to be got -from a pond of water that is low down. - - -_A Cross-bow bent. A Watch wound up._ - -36. In both of the illustrations now given, we have used the force of -gravity as that force against which we are to do work, and in virtue -of which a stone high up, or a head of water, is in a position of -advantage, and has the power of doing work as it falls to a lower -level. But there are other forces besides gravity, and, with respect to -these, bodies may be in a position of advantage and be able to do work -just as truly as the stone, or the head of water, in the case before -mentioned. - -Let us take, for instance, the force of elasticity, and consider what -happens in a cross-bow. When this is bent, the bolt is evidently in a -position of advantage with regard to the elastic force of the bow; and -when it is discharged, this energy of position of the bolt is converted -into energy of motion, just as, when a stone on the top of a house -is allowed to fall, its energy of position is converted into that of -actual motion. - -In like manner a watch wound up is in a position of advantage with -respect to the elastic force of the mainspring, and as the wheels of -the watch move this is gradually converted into energy of motion. - - -_Advantage of Position._ - -37. It is, in fact, the fate of all kinds of energy of position to be -ultimately converted into energy of motion. - -The former may be compared to money in a bank, or capital, the latter -to money which we are in the act of spending; and just as, when we have -money in a bank, we can draw it out whenever we want it, so, in the -case of energy of position, we can make use of it whenever we please. -To see this more clearly, let us compare together a watermill driven by -a head of water, and a windmill driven by the wind. In the one case we -may turn on the water whenever it is most convenient for us, but in the -other we must wait until the wind happens to blow. The former has all -the independence of a rich man; the latter, all the obsequiousness of -a poor one. If we pursue the analogy a step further, we shall see that -the great capitalist, or the man who has acquired a lofty position, is -respected because he has the disposal of a great quantity of energy; -and that whether he be a nobleman or a sovereign, or a general in -command, he is powerful only from having something which enables him -to make use of the services of others. When the man of wealth pays a -labouring man to work for him, he is in truth converting so much of -his energy of position into actual energy, just as a miller lets out a -portion of his head of water in order to do some work by its means. - - -_Transmutations of Visible Energy.--A Kilogramme shot upwards._ - -38. We have thus endeavoured to show that there is an energy of repose -as well as a living energy, an energy of position as well as of motion; -and now let us trace the changes which take place in the energy of a -weight, shot vertically upwards, as it continues to rise. It starts -with a certain amount of energy of motion, but as it ascends, this is -by degrees changed into that of position, until, when it gets to the -top of its flight, its energy is entirely due to position. - -To take an example, let us suppose that a kilogramme is projected -vertically upwards with the velocity of 19·6 metres in one second. -According to the formula of Art. 28, it contains 19·6 units of energy -due to its actual velocity. - -If we examine it at the end of one second, we shall find that it has -risen 14·7 metres in height, and has now the velocity of 9·8. This -velocity we know (Art. 26) denotes an amount of actual energy equal -to 4·9, while the height reached corresponds to an energy of position -equal to 14·7. The kilogramme has, therefore, at this moment a total -energy of 19·6, of which 14·7 units are due to position, and 4·9 to -actual motion. - -If we next examine it at the end of another second, we shall find that -it has just been brought to rest, so that its energy of motion is -_nil_; nevertheless, it has succeeded in raising itself 19·6 metres in -height, so that its energy of position is 19·6. - -There is, therefore, no disappearance of energy during the rise of -the kilogramme, but merely a gradual change from one kind to another. -It starts with actual energy, and this is gradually changed into that -of position; but if, at any stage of its ascent, we add together the -actual energy of the kilogramme, and that due to its position, we shall -find that their sum always remains the same. - -39. Precisely the reverse takes place when the kilogramme begins its -descent. It starts on its downward journey with no energy of motion -whatever, but with a certain amount of energy of position; as it falls, -its energy of position becomes less, and its actual energy greater, the -sum of the two remaining constant throughout, until, when it is about -to strike the ground, its energy of position has been entirely changed -into that of actual motion, and it now approaches the ground with the -velocity, and, therefore, with the energy, which it had when it was -originally projected upwards. - - -_The Inclined Plane._ - -40. We have thus traced the transmutations, as regards energy, of a -kilogramme shot vertically upwards, and allowed to fall again to the -earth, and we may now vary our hypothesis by making the kilogramme -rise vertically, but descend by means of a smooth inclined plane -without friction--imagine in fact, the kilogramme to be shaped like a -ball or roller, and the plane to be perfectly smooth. Now, it is well -known to all students of dynamics, that in such a case the velocity -which the kilogramme has when it has reached the bottom of the plane -will be equal to that which it would have had if it had been dropped -down vertically through the same height, and thus, by introducing a -smooth inclined plane of this kind, you neither gain nor lose anything -as regards energy. - -In the first place, you do not gain, for think what would happen if the -kilogramme, when it reached the bottom of the inclined plane, should -have a greater velocity than you gave it originally, when you shot it -up. It would evidently be a profitable thing to shoot up the kilogramme -vertically, and bring it down by means of the plane, for you would get -back more energy than you originally spent upon it, and in every sense -you would be a gainer. You might, in fact, by means of appropriate -apparatus, convert the arrangement into a perpetual motion machine, and -go on accumulating energy without limit--but this is not possible. - -On the other hand, the inclined plane, unless it be rough and angular, -will not rob you of any of the energy of the kilogramme, but will -restore to you the full amount, when once the bottom has been reached. -Nor does it matter what be the length or shape of the plane, or -whether it be straight, or curved, or spiral, for in all cases, if it -only be smooth and of the same vertical height, you will get the same -amount of energy by causing the kilogramme to fall from the top to the -bottom. - -41. But while the energy remains the same, the time of descent will -vary according to the length and shape of the plane, for evidently the -kilogramme will take a longer time to descend a very sloping plane -than a very steep one. In fact, the sloping plane will take longer to -generate the requisite velocity than the steep one, but both will have -produced the same result as regards energy, when once the kilogramme -has arrived at the bottom. - - -_Functions of a Machine._ - -42. Our readers are now beginning to perceive that energy cannot be -created, and that by no means can we coax or cozen Dame Nature into -giving us back more than we are entitled to get. To impress this -fundamental principle still more strongly upon our minds, let us -consider in detail one or two mechanical contrivances, and see what -they amount to as regards energy. - -[Illustration: Fig. 1.] - -Let us begin with the second system of pulleys. Here we have a power -P attached to the one end of a thread, which passes over all the -pulleys, and is ultimately attached, by its other extremity, to a -hook in the upper or fixed block. The weight W is, on the other hand, -attached to the lower or moveable block, and rises with it. Let us -suppose that the pulleys are without weight and the cords without -friction, and that W is supported by six cords, as in the figure. -Now, when there is equilibrium in this machine, it is well known -that W will be equal to six times P; that is to say, a power of one -kilogramme will, in such a machine, balance or support a weight of six -kilogrammes. If P be increased a single grain more, it will overbalance -W, and P will descend, while W will begin to rise. In such a case, -after P has descended, say six metres, its weight being, say, one -kilogramme, it has lost a quantity of energy of position equal to six -units, since it is at a lower level by six metres than it was before. -We have, in fact, expended upon our machine six units of energy. Now, -what return have we received for this expenditure? Our return is -clearly the rise of W, and mechanicians will tell us that in this case -W will have risen one metre. - -But the weight of W is six kilogrammes, and this having been raised -one metre represents an energy of position equal to six. We have thus -spent upon our machine, in the fall of P, an amount of energy equal to -six units, and obtained in the rise of W an equivalent amount equal to -six units also. We have, in truth, neither gained nor lost energy, but -simply changed it into a form more convenient for our use. - -[Illustration: Fig. 2.] - -43. To impress this truth still more strongly, let us take quite a -different machine, such as the hydrostatic press. Its mode of action -will be perceived from Fig. 2. Here we have two cylinders, a wide and -a narrow one, which are connected together at the bottom by means of -a strong tube. Each of these cylinders is provided with a water-tight -piston, the space beneath being filled with water. It is therefore -manifest, since the two cylinders are connected together, and since -water is incompressible, that when we push down the one piston the -other will be pushed up. Let us suppose that the area of the small -piston is one square centimetre,[3] and that of the large piston -one hundred square centimetres, and let us apply a weight of ten -kilogrammes to the smaller piston. Now, it is known, from the laws of -hydrostatics, that every square centimetre of the larger piston will be -pressed upwards with the force of ten kilogrammes, so that the piston -will altogether mount with the force of 1000 kilogrammes--that is to -say, it will raise a weight of this amount as it ascends. - -Here, then, we have a machine in virtue of which a pressure of ten -kilogrammes on the small piston enables the large piston to rise with -the force of 1000 kilogrammes. But it is very easy to see that, while -the small piston falls one metre, the large one will only rise one -centimetre. For the quantity of water under the pistons being always -the same, if this be pushed down one metre in the narrow cylinder, it -will only rise one centimetre in the wide one. - -Let us now consider what we gain by this machine. The power of ten -kilogrammes applied to the smaller piston is made to fall through one -metre, and this represents the amount of energy which we have expended -upon our machine, while, as a return, we obtain 1000 kilogrammes raised -through one single centimetre. Here, then, as in the case of the -pulleys, the return of energy is precisely the same as the expenditure, -and, provided we ignore friction, we neither gain nor lose anything -by the machine. All that we do is to transmute the energy into a -more convenient form--what we gain in power we lose in space; but we -are willing to sacrifice space or quickness of motion in order to -obtain the tremendous pressure or force which we get by means of the -hydrostatic press. - - -_Principle of Virtual Velocities._ - -44. These illustrations will have prepared our readers to perceive the -true function of a machine. This was first clearly defined by Galileo, -who saw that in any machine, no matter of what kind, if we raise a -large weight by means of a small one, it will be found that the small -weight, multiplied into the space through which it is lowered, will -exactly equal the large weight, multiplied into that through which it -is raised. - -This principle, known as that of virtual velocities, enables us to -perceive at once our true position. We see that the world of mechanism -is not a manufactory, in which energy is created, but rather a mart, -into which we may bring energy of one kind and change or barter it -for an equivalent of another kind, that suits us better--but if we -come with nothing in our hand, with nothing we shall most assuredly -return. A machine, in truth, does not create, but only transmutes, and -this principle will enable us to tell, without further knowledge of -mechanics, what are the conditions of equilibrium of any arrangement. - -For instance, let it be required to find those of a lever, of which the -one arm is three times as long as the other. Here it is evident that if -we overbalance the lever by a single grain, so as to cause the long arm -with its power to fall down while the short one with its weight rises -up, then the long arm will fall three inches for every inch through -which the short arm rises; and hence, to make up for this, a single -kilogramme on the long arm will balance three kilogrammes on the short -one, or the power will be to the weight as one is to three. - -[Illustration: Fig. 3.] - -45. Or, again, let us take the inclined plane as represented in Fig. -3. Here we have a smooth plane and a weight held upon it by means of a -power P, as in the figure. Now, if we overbalance P by a single grain, -we shall bring the weight W from the bottom to the top of the plane. -But when this has taken place, it is evident that P has fallen through -a vertical distance equal to the length of the plane, while on the -other hand W has only risen through a vertical distance equal to the -height. Hence, in order that the principle of virtual velocities shall -hold, we must have P multiplied into its fall equal to W multiplied -into its rise, that is to say, - - P × Length of plane = W × Height of plane, - - or P/W = (Height.)/(Length.) - - -_What Friction does._ - -46. The two examples now given are quite sufficient to enable our -readers to see the true function of a machine, and they are now -doubtless disposed to acknowledge that no machine will give back more -energy than is spent upon it. It is not, however, equally clear that -it will not give back less; indeed, it is a well-known fact that it -constantly does so. For we have supposed our machine to be without -friction--but no machine is without friction--and the consequence is -that the available out-come of the machine is more or less diminished -by this drawback. Now, unless we are able to see clearly what part -friction really plays, we cannot prove the conservation of energy. -We see clearly enough that energy cannot be created, but we are -not equally sure that it cannot be destroyed; indeed, we may say -we have apparent grounds for believing that it is destroyed--that -is our present position. Now, if the theory of the conservation -of energy be true--that is to say, if energy is in any sense -indestructible--friction will prove itself to be, not the destroyer -of energy, but merely the converter of it into some less apparent and -perhaps less useful form. - -47. We must, therefore, prepare ourselves to study what friction really -does, and also to recognize energy in a form remote from that possessed -by a body in visible motion, or by a head of water. To friction we may -add percussion, as a process by which energy is apparently destroyed; -and as we have (Art. 39) considered the case of a kilogramme shot -vertically upwards, demonstrating that it will ultimately reach the -ground with an energy equal to that with which it was shot upwards, -we may pursue the experiment one step further, and ask what becomes -of its energy after it has struck the ground and come to rest? We -may vary the question by asking what becomes of the energy of the -smith’s blow after his hammer has struck the anvil, or what of the -energy of the cannon ball after it has struck the target, or what of -that of the railway train after it has been stopped by friction at -the break-wheel? All these are cases in which percussion or friction -appears at first sight to have destroyed visible energy; but before -pronouncing upon this seeming destruction, it clearly behoves us to ask -if anything else makes its appearance at the moment when the visible -energy is apparently destroyed. For, after all, energy may be like the -Eastern magicians, of whom we read that they had the power of changing -themselves into a variety of forms, but were nevertheless very careful -not to disappear altogether. - - -_When Motion is destroyed, Heat appears._ - -48. Now, in reply to the question we have put, it may be confidently -asserted that whenever visible energy is apparently destroyed by -percussion or friction, something else makes its appearance, and that -something is _heat_. Thus, a piece of lead placed upon an anvil may -be greatly heated by successive blows of a blacksmith’s hammer. The -collision of flint and steel will produce heat, and a rapidly-moving -cannon ball, when striking against an iron target, may even be heated -to redness. Again, with regard to friction, we know that on a dark -night sparks are seen to issue from the break-wheel which is stopping a -railway train, and we know, also, that the axles of railway carriages -get alarmingly hot, if they are not well supplied with grease. - -Finally, the schoolboy will tell us that he is in the habit of rubbing -a brass button upon the desk, and applying it to the back of his -neighbour’s hand, and that when his own hand has been treated in this -way, he has found the button unmistakeably hot. - - -_Heat a species of Motion._ - -49. For a long time this appearance of heat by friction or percussion -was regarded as inexplicable, because it was believed that heat was -a kind of matter, and it was difficult to understand where all this -heat came from. The partisans of the material hypothesis, no doubt, -ventured to suggest that in such processes heat might be drawn from the -neighbouring bodies, so that the Caloric (which was the name given to -the imaginary substance of heat) was squeezed or rubbed out of them, -according as the process was percussion or friction. But this was -regarded by many as no explanation, even before Sir Humphry Davy, about -the end of last century, clearly showed it to be untenable. - -50. Davy’s experiments consisted in rubbing together two pieces of ice -until it was found that both were nearly melted, and he varied the -conditions of his experiments in such a manner as to show that the heat -produced in this case could not be abstracted from the neighbouring -bodies. - -51. Let us pause to consider the alternatives to which we are driven -by this experiment. If we still choose to regard heat as a substance, -since this has not been taken from the surrounding bodies, it must -necessarily have been created in the process of friction. But if we -choose to regard heat as a species of motion, we have a simpler -alternative, for, inasmuch as the energy of visible motion has -disappeared in the process of friction, we may suppose that it has been -transformed into a species of molecular motion, which we call heat; and -this was the conclusion to which Davy came. - -52. About the same time another philosopher was occupied with a similar -experiment. Count Rumford was superintending the boring of cannon at -the arsenal at Munich, and was forcibly struck with the very great -amount of heat caused by this process. The source of this heat appeared -to him to be absolutely inexhaustible, and, being unwilling to regard -it as the creation of a species of matter, he was led like Davy to -attribute it to motion. - -53. Assuming, therefore, that heat is a species of motion, the next -point is to endeavour to comprehend what kind of motion it is, and in -what respects it is different from ordinary visible motion. To do this, -let us imagine a railway carriage, full of passengers, to be whirling -along at a great speed, its occupants quietly at ease, because, -although they are in rapid motion, they are all moving at the same rate -and in the same direction. Now, suppose that the train meets with a -sudden check;--a disaster is the consequence, and the quiet placidity -of the occupants of the carriage is instantly at an end. - -Even if we suppose that the carriage is not broken up and its occupants -killed, yet they are all in a violent state of excitement; those -fronting the engine are driven with force against their opposite -neighbours, and are, no doubt, as forcibly repelled, each one taking -care of himself in the general scramble. Now, we have only to -substitute particles for persons, in order to obtain an idea of what -takes place when percussion is converted into heat. We have, or suppose -we have, in this act the same violent collision of atoms, the same -thrusting forward of A upon B, and the same violence in pushing back on -the part of B--the same struggle, confusion, and excitement--the only -difference being that particles are heated instead of human beings, or -their tempers. - -54. We are bound to acknowledge that the proof which we have now given -is not a direct one; indeed, we have, in our first chapter, explained -the impossibility of our ever seeing these individual particles, or -watching their movements; and hence our proof of the assertion that -heat consists in such movements cannot possibly be direct. We cannot -see that it does so consist, but yet we may feel sure, as reasonable -beings, that we are right in our conjecture. - -In the argument now given, we have only two alternatives to start -with--either heat must consist of a motion of particles, or, when -percussion or friction is converted into heat, a peculiar substance -called caloric must be created, for if heat be not a species of motion -it must necessarily be a species of matter. Now, we have preferred to -consider heat as a species of motion to the alternative of supposing -the creation of a peculiar kind of matter. - -55. Nevertheless, it is desirable to have something to say to an -opponent who, rather than acknowledge heat to be a species of motion, -will allow the creation of matter. To such an one we would say that -innumerable experiments render it certain that a hot body is not -sensibly heavier than a cold one, so that if heat be a species of -matter it is one that is not subject to the law of gravity. If we burn -iron wire in oxygen gas, we are entitled to say that the iron combines -with the oxygen, because we know that the product is heavier than the -original iron by the very amount which the gas has lost in weight. But -there is no such proof that during combustion the iron has combined -with a substance called caloric, and the absence of any such proof is -enough to entitle us to consider heat to be a species of motion, rather -than a species of matter. - - -_Heat a Backward and Forward Motion._ - -56. We shall now suppose that our readers have assented to our -proposition that heat is a species of motion. It is almost unnecessary -to add that it must be a species of backward and forward motion; for -nothing is more clear than that _a heated substance is not in motion as -a whole_, and will not, if put upon a table, push its way from the one -end to the other. - -Mathematicians express this peculiarity by saying that, although there -is violent internal motion among the particles, yet the centre of -gravity of the substance remains at rest; and since, for most purposes, -we may suppose a body to act as if concentrated at its centre of -gravity, we may say that the body is at rest. - -57. Let us here, before proceeding further, borrow an illustration from -that branch of physics which treats of sound. Suppose, for instance, -that a man is accurately balanced in a scale-pan, and that some water -enters his ear; of course he will become heavier in consequence, and if -the balance be sufficiently delicate, it will exhibit the difference. -But suppose a sound or a noise enters his ear, he may say with truth -that something has entered, but yet that something is not matter, nor -will he become one whit heavier in consequence of its entrance, and he -will remain balanced as before. Now, a man into whose ear sound has -entered may be compared to a substance into which heat has entered; -we may therefore suppose a heated body to be similar in many respects -to a sounding body, and just as the particles of a sounding body move -backwards and forwards, so we may suppose that the particles of a -heated body do the same. - -We shall take another opportunity (Art. 162) to enlarge upon this -likeness; but, meanwhile, we shall suppose that our readers perceive -the analogy. - - -_Mechanical Equivalent of Heat._ - -58. We have thus come to the conclusion that when any heavy body, say -a kilogramme weight, strikes the ground, the visible energy of the -kilogramme is changed into heat; and now, having established the fact -of a relationship between these two forms of energy, our next point -is to ascertain according to what law the heating effect depends upon -the height of fall. Let us, for instance, suppose that a kilogramme of -water is allowed to drop from the height of 848 metres, and that we -have the means of confining to its own particles and retaining there -the heating effect produced. Now, we may suppose that its descent -is accomplished in two stages; that, first of all, it falls upon a -platform from the height of 424 metres, and gets heated in consequence, -and that then the heated mass is allowed to fall other 424 metres. It -is clear that the water will now be doubly heated; or, in other words, -the heating effect in such a case will be proportional to the height -through which the body falls--that is to say, it will be proportional -to the actual energy which the body possesses before the blow has -changed this into heat. In fact, just as the actual energy represented -by a fall from a height is proportional to the height, so is the -heating effect, or molecular energy, into which the actual energy is -changed proportional to the height also. Having established this point, -we now wish to know through how many metres a kilogramme of water must -fall in order to be heated one degree centigrade. - -59. For a precise determination of this important point, we are -indebted to Dr. Joule, of Manchester, who has, perhaps, done more than -any one else to put the science of energy upon a sure foundation. Dr. -Joule made numerous experiments, with the view of arriving at the -exact relation between mechanical energy and heat; that is to say, of -determining the mechanical equivalent of heat. In some of the most -important of these he took advantage of the friction of fluids. - -[Illustration: Fig. 4.] - -60. These experiments were conducted in the following manner. A certain -fixed weight was attached to a pulley, as in the figure. The weight -had, of course, a tendency to descend, and hence to turn the pulley -round. The pulley had its axle supported upon friction wheels, at _f_ -and _f_, by means of which the friction caused by the movement of the -pulley was very much reduced. A string, passing over the circumference -of the pulley, was wrapped round _r_, so that, as the weight descended, -the pulley moved round, and the string of the pulley caused _r_ to -rotate very rapidly. Now, the motion of the axis _r_ was conducted -within the covered box B, where there was attached to _r_ a system of -paddles, of which a sketch is given in figure; and therefore, as _r_ -moved, these paddles moved also. There were, altogether, eight sets of -these paddles revolving between four stationary vanes. If, therefore, -the box were full of liquid, the paddles and the vanes together would -churn it about, for these stationary vanes would prevent the liquid -being carried along by the paddles in the direction of rotation. - -Now, in this experiment, the weight was made to descend through a -certain fixed distance, which was accurately measured. As it descended, -the paddles were set in motion, and the energy of the descending weight -was thus made to churn, and hence to heat some water contained in the -box B. When the weight had descended a certain distance, by undoing a -small peg _p_, it could be wound up again without moving the paddles -in B, and thus the heating effect of several falls of the weight could -be accumulated until this became so great as to be capable of being -accurately measured by a thermometer. It ought to be mentioned that -great care was taken in these experiments, not only to reduce the -friction of the axles of the pulley as much as possible, but also to -estimate and correct for this friction as accurately as possible; in -fact, every precaution was taken to make the experiment successful. - -61. Other experiments were made by Joule, in some of which a disc was -made to rotate against another disc of cast-iron pressed against it, -the whole arrangement being immersed in a cast-iron vessel filled -with mercury. From all these experiments, Dr. Joule concluded that -the quantity of heat produced by friction, if we can preserve and -accurately measure it, will always be found proportional to the -quantity of work expended. He expressed this proportion by stating the -number of units of work in kilogrammetres necessary to raise by 1° C. -the temperature of one kilogramme of water. This was 424, as determined -by his last and most complete experiments; and hence we may conclude -that if a kilogramme of water be allowed to fall through 424 metres, -and if its motion be then suddenly stopped, sufficient heat will be -generated to raise the temperature of the water through 1° C., and so -on, in the same proportion. - -62. Now, if we take the kilogrammetre as our unit of work, and the heat -necessary to raise a kilogramme of water 1° C. as our unit of heat, -this proportion may be expressed by saying that _one heat unit is equal -to 424 units of work_. - -This number is frequently spoken of as the mechanical equivalent of -heat; and in scientific treatises it is denoted by J., the initial of -Dr. Joule’s name. - -63. We have now stated the exact relationship that subsists between -mechanical energy and heat, and before proceeding further with proofs -of the great law of conservation, we shall endeavour to make our -readers acquainted with other varieties of energy, on the ground that -it is necessary to penetrate the various disguises that our magician -assumes before we can pretend to explain the principles that actuate -him in his transformations. - - -FOOTNOTES: - -[3] That is to say, a square the side of which is one centimetre, or -the hundredth part of a metre. - - - - -CHAPTER III. - -_THE FORCES AND ENERGIES OF NATURE: THE LAW OF CONSERVATION._ - - -64. In the last chapter we introduced our readers to two varieties of -energy, one of them visible, and the other invisible or molecular; and -it will now be our duty to search through the whole field of physical -science for other varieties. Here it is well to bear in mind that all -energy consists of two kinds, that of _position_ and that of _actual -motion_, and also that this distinction holds for invisible molecular -energy just as truly as it does for that which is visible. Now, energy -of position implies a body in a position of advantage with respect -to some force, and hence we may with propriety begin our search by -investigating the various forces of nature. - - -_Gravitation._ - -65. The most general, and perhaps the most important, of these -forces is _gravitation_, and the law of action of this force may be -enunciated as follows:--_Every particle of the universe attracts every -other particle with a force depending jointly upon the mass of the -attracting and of the attracted particle, and varying inversely as the -square of distance between the two._ A little explanation will make -this plain. - -Suppose a particle or system of particles of which the mass is unity to -be placed at a distance equal to unity from another particle or system -of particles of which the mass is also unity--the two will attract each -other. Let us agree to consider the mutual attraction between them -equal to unity also. - -Suppose, now, that we have on the one side two such systems with a mass -represented by 2, and on the other side the same system as before, -with a mass represented by unity, the distance, meanwhile, remaining -unaltered. It is clear the double system will now attract the single -system with a twofold force. Let us next suppose the mass of both -systems to be doubled, the distance always remaining the same. It is -clear that we shall now have a fourfold force, each unit of the one -system attracting each unit of the other. In like manner, if the mass -of the one system is 2, and that of the other 3, the force will be 6. -We may, for instance, call the components of the one system A_{1}, -A₂, and those of the other A_{3}, A_{4}, A_{5}, and we shall have -A_{1} pulled towards A_{3}, A_{4}, and A_{5}, with a threefold force, -and A₂ pulled towards A_{3}, A_{4}, and A_{5}, with a threefold -force, making altogether a force equal to 6. - -In the next place, let the masses remain unaltered, but let the -distance between them be doubled, then the force will be reduced -fourfold. Let the distance be tripled, then the force will be reduced -ninefold, and so on. - -66. Gravitation may be described as a very weak force, capable of -acting at a distance, or at least of appearing to do so. It takes the -mass of the whole earth to produce the force with which we are so -familiar at its surface, and the presence of a large mass of rock or -mountain does not produce any appreciable difference in the weight of -any substance. It is the gravitation of the earth, lessened of course -by distance, which acts upon the moon 240,000 miles away, and the -gravitation of the sun influences in like manner the earth and the -various other planets of our system. - - -_Elastic Forces._ - -67. Elastic forces, although in their mode of action very different -from gravity, are yet due to visible arrangements of matter; thus, -when a cross-bow is bent, there is a visible change produced in the -bow, which, as a whole, resists this bending, and tends to resume its -previous position. It therefore requires energy to bend a bow, just as -truly and visibly as it does to raise a weight above the earth, and -elasticity is, therefore, as truly a species of force as gravity is. -We shall not here attempt to discuss the various ways in which this -force may act, or in which a solid elastic substance will resist all -attempts to deform it; but in all cases it is clearly manifest that -work must be spent upon the body, and the force of elasticity must be -encountered and overcome throughout a certain space before any sensible -deformation can take place. - - -_Force of Cohesion._ - -68. Let us now leave the forces which animate large masses of matter, -and proceed to discuss those which subsist between the smaller -particles of which these large masses are composed. And here we must -say one word more about molecules and atoms, and the distinction we -feel ourselves entitled to draw between these very small bodies, even -although we shall never be able to see either the one or the other. - -In our first chapter (Art. 7) we supposed the continual sub-division of -a grain of sand until we had arrived at the smallest entity retaining -all the properties of sand--this we called a _molecule_, and nothing -smaller than this is entitled to be called sand. If we continue this -sub-division further, the molecule of sand separates itself into its -chemical constituents, consisting of silicon on the one side, and -oxygen on the other. Thus we arrive at last at the smallest body which -can call itself silicon, and the smallest which can call itself oxygen, -and we have no reason to suppose that either of these is capable of -sub-division into something else, since we regard oxygen and silicon as -elementary or simple bodies. Now, these constituents of the silicon -molecule are called _atoms_, so that we say the sand molecule is -divisible into atoms of silicon and of oxygen. Furthermore, we have -strong reason for supposing that such molecules and atoms really exist, -but into the arguments for their existence we cannot now enter--it is -one of those things that we must ask our readers to take for granted. - -69. Let us now take two molecules of sand. These, when near together, -have a very strong attraction for each other. It is, in truth, this -attraction which renders it difficult to break up a crystalline -particle of sand or rock crystal. But it is only exerted when the -molecules are near enough together to form a homogeneous crystalline -structure, for let the distance between them be somewhat increased, and -we find that all attraction entirely vanishes. Thus there is little -or no attraction between different particles of sand, even although -they are very closely packed together. In like manner, the integrity -of a piece of glass is due to the attraction between its molecules; -but let these be separated by a flaw, and it will soon be found that -this very small increase of distance greatly diminishes the attraction -between the particles, and that the structure will now fall to pieces -from the slightest cause. Now, these examples are sufficient to show -that molecular attraction or _cohesion_, as this is called, is a force -which acts very powerfully through a certain small distance, but which -vanishes altogether when this distance becomes perceptible. Cohesion -is strongest in solids, while in liquids it is much diminished, and in -gases it may be said to vanish altogether. The molecules of gases are, -in truth, so far away from one another, as to have little or no mutual -attraction, a fact proved by Dr. Joule, whose name was mentioned in the -last chapter. - - -_Force of Chemical Affinity._ - -70. Let us now consider the mutual forces between atoms. These may be -characterized as even stronger than the forces between molecules, but -as disappearing still more rapidly when the distance is increased. Let -us, for instance, take carbon and oxygen--two substances which are -ready to combine together to form carbonic acid, whenever they have a -suitable opportunity. In this case, each atom of carbon will unite with -two of oxygen, and the result will be something quite different from -either. Yet under ordinary circumstances carbon, or its representative, -coal, will remain unchanged in the presence of oxygen, or of -atmospheric air containing oxygen. There will be no tendency to combine -together, because although the particles of the oxygen would appear to -be in immediate contact with those of the carbon, yet the nearness is -not sufficient to permit of chemical affinity acting with advantage. -When, however, the nearness becomes sufficient, then chemical affinity -begins to operate. We have, in fact, the familiar act of combustion, -and, as its consequence, the chemical union of the carbon or coal with -the oxygen of the air, carbonic acid being the result. Here, then, we -have a very powerful force acting only at a very small distance, which -we name _chemical affinity_, inasmuch as it represents the attraction -exerted between atoms of different bodies in contradistinction to -cohesion, which denotes the attraction between molecules of the same -body. - -71. If we regard gravitation as the representative of forces that act -or appear to act, at a distance, we may regard cohesion and chemical -affinity as the representatives of those forces which, although very -powerful, only act or appear to act through a very small interval of -distance. - -A little reflection will show us how inconvenient it would be if -gravitation diminished very rapidly with the distance; for then -even supposing that the bond which retains us to the earth were to -hold good, that which retains the moon to the earth might vanish -entirely, as well as that which retains the earth to the sun, and the -consequences would be far from pleasant. Reflection will also show -us how inconvenient it would be if chemical affinity existed at all -distances; if coal, for instance, were to combine with oxygen without -the application of heat, it would greatly alter the value of this fuel -to mankind, and would materially check the progress of human industry. - - -_Remarks on Molecular and Atomic Forces._ - -72. Now, it is important to remember that we must treat cohesion and -chemical affinity exactly in the same way as gravity has been treated; -and just as we have energy of position with respect to gravity, so -may we have as truly a species of energy of position with respect to -cohesion and chemical affinity. Let us begin with cohesion. - -73. We have hitherto regarded heat as a peculiar motion of the -molecules of matter, without any reference to the force which actuates -these molecules. But it is a well-known fact that bodies in general -expand when heated, so that, in virtue of this expansion, the molecules -of a body are driven violently apart against the force of cohesion. -Work has in truth been done against this force, just as truly as, when -a kilogramme is raised from the earth, work is done against the force -of gravity. When a substance is heated, we may, therefore, suppose that -the heat has a twofold office to perform, part of it going to increase -the actual motions of the molecules, and part of it to separate these -molecules from one another against the force of cohesion. Thus, if I -swing round horizontally a weight (attached to my hand by an elastic -thread of india-rubber), my energy will be spent in two ways--first -of all, it will be spent in communicating a velocity to the weight; -and, secondly, in stretching the india-rubber string, by means of the -centrifugal tendency of the weight. Work will be done against the -elastic force of the string, as well as spent in increasing the motion -of the weight. - -Now, something of this kind may be taking place when a body is heated, -for we may very well suppose heat to consist of a vertical or circular -motion, the tendency of which would be to drive the particles asunder -against the force of cohesion. Part, therefore, of the energy of heat -will be spent in augmenting the motion, and part in driving asunder the -particles. We may, however, suppose that, in ordinary cases, the great -proportion of the energy of heat goes towards increasing the molecular -motion, rather than in doing work against the force of cohesion. - -74 In certain cases, however, it is probable that the greater part -of the heat applied is spent in doing work against molecular forces, -instead of increasing the motions of molecules. - -Thus, when a solid melts, or when a liquid is rendered gaseous, a -considerable amount of heat is spent in the process, which does not -become sensible, that is to say, does not affect the thermometer. Thus, -in order to melt a kilogramme of ice, heat is required sufficient to -raise a kilogramme of water through 80° C., and yet, when melted, the -water is no warmer than the ice. We express this fact by saying that -the latent heat of water is 80. Again, if a kilogramme of water at -100° be converted entirely into steam, as much heat is required as -would raise the water through 537° C., or 537 kilogrammes of water -through one degree; but yet the steam is no hotter than the water, and -we express this fact by saying that the latent heat of steam is 537. -Now, in both of these instances it is at least extremely probable that -a large portion of the heat is spent in doing work against the force -of cohesion; and, more especially, when a fluid is converted into a -gas, we know that the molecules are in that process separated so far -from one another as to lose entirely any trace of mutual force. We may, -therefore, conclude that although in most cases the greater portion of -the heat applied to a body is spent in increasing its molecular motion, -and only a small part in doing work against cohesion, yet when a solid -melts, or a liquid vaporizes, a large portion of the heat required -is not improbably spent in doing work against molecular forces. But -the energy, though spent, is not lost, for when the liquid again -freezes, or when the vapour again condenses, this energy is once more -transformed into the shape of sensible heat, just as when a stone is -dropped from the top of a house, its energy of position is transformed -once more into actual energy. - -75. A single instance will suffice to give our readers a notion of -the strength of molecular forces. If a bar of wrought iron, whose -temperature is 10° C. above that of the surrounding medium, be tightly -secured at its extremities, it will draw these together with a force of -at least one ton for each square inch of section. In some cases where -a building has shown signs of bulging outwards, iron bars have been -placed across it, and secured while in a heated state to the walls. -On cooling, the iron contracted with great force, and the walls were -thereby pulled together. - -76. We are next brought to consider atomic forces, or those which lead -to chemical union, and now let us see how these are influenced by heat. -We have seen that heat causes a separation between the molecules of a -body, that is to say, it increases the distance between two contiguous -molecules, but we must not suppose that, meanwhile, the molecules -themselves are left unaltered. - -The tendency of heat to cause separation is not confined to increasing -the distance between molecules, but acts also, no doubt, in increasing -the distance between parts of the same molecule: in fact, the energy -of heat is spent in pulling the constituent atoms asunder against the -force of chemical affinity, as well as in pulling the molecules asunder -against the force of cohesion, so that, at a very high temperature, it -is probable that most chemical compounds would be decomposed, and many -are so, even at a very moderate heat. - -Thus the attraction between oxygen and silver is so slight that at -a comparatively low temperature the oxide of silver is decomposed. -In like manner, limestone, or carbonate of lime, is decomposed when -subjected to the heat of a lime-kiln, carbonic acid being given off, -while quick-lime remains behind. Now, in separating heterogeneous -atoms against the powerful force of chemical affinity, work is done as -truly as it is in separating molecules from one another against the -force of cohesion, or in separating a stone from the earth against the -force of gravity. - -77. Heat, as we have seen, is very frequently influential in performing -this separation, and its energy is spent in so doing; but other -energetic agents produce chemical decomposition as well as heat. For -instance, certain rays of the sun decompose carbonic acid into carbon -and oxygen in the leaves of plants, and their energy is spent in the -process; that is to say, it is spent in pulling asunder two such -powerfully attracting substances against the affinity they have for one -another. And, again, the electric current is able to decompose certain -substances, and of course its energy is spent in the process. - -Therefore, whenever two powerfully attracting atoms are separated, -energy is spent in causing this separation as truly as in separating -a stone from the earth, and when once the separation has been -accomplished we have a species of energy of position just as truly as -we have in a head of water, or in a stone at the top of a house. - -78. It is this chemical separation that is meant when we speak of coal -as a source of energy. Coal, or carbon, has a great attraction for -oxygen, and whenever heat is applied the two bodies unite together. -Now oxygen, as it exists in the atmosphere, is the common inheritance -of all, and if, in addition to this, some of us possess coal in our -cellars, or in pits, we have thus secured a store of energy of -position which we can draw upon with more facility than if it were a -head of water, for, although we can draw upon the energy of a head of -water whenever we choose, yet we cannot carry it about with us from -place to place as we can with coal. We thus perceive that it is not -the coal, by itself, that forms the source of energy, but this is due -to the fact that we have coal, or carbon, in one place, and oxygen in -another, while we have also the means of causing them to unite with -each other whenever we wish. If there were no oxygen in the air, coal -by itself would be of no value. - - -_Electricity: its Properties._ - -79. Our readers have now been told about the force of cohesion that -exists between molecules of the same body, and also about that of -chemical affinity existing between atoms of different bodies. Now, -heterogeneity is an essential element of this latter force--there must -be a difference of some kind before it can exhibit itself--and under -these circumstances its exhibitions are frequently characterized by -very extraordinary and interesting phenomena. - -We allude to that peculiar exhibition arising out of the forces -of heterogeneous bodies which we call _electricity_, and, before -proceeding further, it may not be out of place to give a short sketch -of the mode of action of this very mysterious, but most interesting, -agent. - -80. The science of electricity is of very ancient origin; but its -beginning was very small. For a couple of thousand years it made little -or no progress, and then, during the course of little more than a -century, developed into the giant which it now is. The ancient Greeks -were aware that amber, when rubbed with silk, had the property of -attracting light bodies; and Dr. Gilbert, about three hundred years -ago, showed that many other things, such as sulphur, sealing-wax, and -glass, have the same property as amber. - -In the progress of the science it came to be known that certain -substances are able to carry away the peculiar influence produced, -while others are unable to do so; the former are called _conductors_, -and the latter _non-conductors, or insulators_, of electricity. To make -the distinction apparent, let us take a metal rod, having a glass stem -attached to it, and rub the glass stem with a piece of silk, care being -taken that both silk and glass are warm and dry. We shall find that the -glass has now acquired the property of attracting little bits of paper, -or elder pith; but only where it has been rubbed, for the peculiar -influence acquired by the glass has not been able to spread itself over -the surface. - -If, however, we take hold of the glass stem, and rub the metal rod, -we may, perhaps, produce the same property in the metal, but it will -spread over the whole, not confining itself to the part rubbed. Thus -we perceive that metal is a conductor, while glass is an insulator, or -non-conductor, of electricity. - -[Illustration: Fig. 5.] - -81. We would next observe that _this influence is of two kinds_. To -prove this, let us perform the following experiment. Let us suspend a -small pith ball by a very slender silk thread, as in Fig. 5. Next, let -us rub a stick of warm, dry glass with a piece of warm silk, and with -this excited stick touch the pith ball. The pith ball, after being -touched, will be repelled by the excited glass. Let us next excite, in -a similar manner, a stick of dry sealing-wax with a piece of warm, dry -flannel, and on approaching this stick to the pith ball it will attract -it, although the ball, in its present state, is repelled by the excited -glass. - -Thus a pith ball, touched by excited glass, is repelled by excited -glass, but attracted by excited sealing-wax. - -In like manner, it might be shown that a pith ball, touched by excited -sealing-wax, will be afterwards repelled by excited sealing-wax, but -attracted by excited glass. - -Now, what the excited glass did to the pith ball, was to communicate to -it part of its own influence, after which the ball was repelled by the -glass; or, in other words, _bodies charged with similar electricities -repel one another_. - -Again, since the pith ball, when charged with the electricity from -glass, was attracted to the electrified sealing-wax, we conclude that -_bodies charged with unlike electricities attract one another_. The -electricity from glass is sometimes called _vitreous_, and that from -sealing-wax _resinous_, electricity, but more frequently the former -is known as _positive_, and the latter as _negative_, electricity--it -being understood that these words do not imply the possession of a -positive nature by the one influence, or of a negative nature by the -other, but are merely terms employed to express the apparent antagonism -which exists between the two kinds of electricity. - -82. The next point worthy of notice is that _whenever one electricity -is produced, just as much is produced of an opposite description_. -Thus, in the case of glass excited by silk, we have positive -electricity developed upon the glass, while we have also negative -electricity developed upon the silk to precisely the same extent. -And, again, when sealing-wax is rubbed with flannel, we have negative -electricity developed upon the sealing-wax, and just as much positive -upon the flannel. - -83. These facts have given rise to a theory of electricity, or at -least to a method of regarding it, which, if not absolutely correct, -seems yet to unite together the various phenomena. According to this -hypothesis, a neutral, unexcited body is supposed to contain a store of -the two electricities combined together, so that whenever such a body -is excited, a separation is produced between the two. The phenomena -which we have described are, therefore, due to this electrical -separation, and inasmuch as the two electricities have a great affinity -for one another, it requires the expenditure of energy to produce this -separation, just as truly as it does to separate a stone from the earth. - -84. Now, it is worthy of note that _electrical separation is only -produced when heterogeneous bodies are rubbed together_. Thus, if -flannel be rubbed upon glass, we have electricity; but if flannel be -rubbed upon glass covered with flannel, we have none. In like manner, -if silk be rubbed upon sealing-wax covered with silk, or, in fine, -if two portions of the same substance be rubbed together, we have no -electricity. - -On the other hand, a very slight difference of texture is sometimes -sufficient to produce electrical separation. Thus, if two pieces of the -same silk ribbon be rubbed together lengthwise, we have no electricity; -but if they be rubbed across each other, the one is positively, and the -other negatively, electrified. - -In fact, this element of heterogeneity is an all important one -in electrical development, and this leads us to conjecture that -_electrical attraction may probably be regarded as peculiarly allied to -that force which we call chemical affinity_. At any rate, electricity -and chemical affinity are only manifested between bodies that are, in -some respects, dissimilar. - -85. The following is a list of bodies arranged according to the -electricity which they develop when rubbed together, each substance -being positively electrified when rubbed with any substance beneath it -in the list. - - 1. Cat’s skin. - 2. Flannel. - 3. Ivory. - 4. Glass. - 5. Silk. - 6. Wood. - 7. Shellac. - 8. Resin. - 9. Metals. - 10. Sulphur. - 11. Caoutchouc. - 12. Gutta-percha. - 13. Gun-cotton. - -Thus, if resin be rubbed with cat’s skin, or with flannel, the -cat’s skin or flannel will be positively, and the resin negatively, -electrified; while if glass be rubbed with silk, the glass will be -positively, and the silk negatively, electrified, and so on. - -86. It is not our purpose here to describe at length the _electrical -machine_, but we may state that it consists of two parts, one for -generating electricity by means of the friction of a rubber against -glass, and another consisting of a system of brass tubes, of -considerable surface, supported on glass stems, for collecting and -retaining the electricity so produced. This latter part of the machine -is called its _prime conductor_. - - -_Electric Induction._ - -[Illustration: Fig. 6.] - -87. Let us now suppose that we have set in action a machine of this -kind, and accumulated a considerable quantity of positive electricity -in its prime conductor at A. Let us next take two vessels, B and C, -made of brass, supported on glass stems. These two vessels are supposed -to be in contact, but at the same time to be capable of being separated -from one another at their middle point, where the line is drawn in Fig. -6. Now let us cause B and C to approach A together. At first, B and C -are not electrified, that is to say, their two electricities are not -separated from each other, but are mixed together; but mark what will -happen as they are pushed towards A. The positive electricity of A will -decompose the two electricities of B and C, attracting the negative -towards itself, and repelling the positive as far away as possible. -The disposition of electricities will, therefore, be as in the figure. -If we now pull C away from B, we have obtained a quantity of positive -electricity on C, by help of the original electricity which was in A; -in fact, we have made use of the original stock or electrical capital -in A, in order to obtain positive electricity in C, without, however, -diminishing the amount of our original stock. Now, this distant action -or help, rendered by the original electricity in separating that of B -and C, is called electric induction. - -88. The experiment may, however, be performed in a somewhat different -manner--we may allow B and C to remain together, and gradually push -them nearer to A. As B and C approach A, the separation of their -electricities will become greater and greater, until, when A and -B are only divided by a small thickness of air, the two opposite -electricities then accumulated will have sufficient strength to rush -together through the air, and unite with each other by means of a spark. - -89. The principle of induction may be used with advantage, when it is -wished to accumulate a large quantity of electricity. - -[Illustration: Fig. 7.] - -In this case, an instrument called a _Leyden jar_ is very frequently -employed. It consists of a glass jar, coated inside and outside with -tin foil, as in Fig. 7. A brass rod, having a knob at the end of it, -is connected metallically with the inside coating, and is kept in its -place by being passed through a cork, which covers the mouth of the -jar. We have thus two metallic coatings which are not electrically -connected with one another. Now, in order to charge a jar of this kind, -let the outside coating be connected by a chain with the earth, while -at the same time positive electricity from the prime conductor of an -electrical machine is communicated to the inside knob. - -The positive electricity will accumulate on the inside coating -with which the knob is connected. It will then decompose the two -electricities of the outside coating, driving the positive electricity -to the earth, and there dissipating it, but attracting the negative -to itself. There will thus be positive electricity on the inside, -and negative on the outside coating. These two electricities may be -compared to two hostile armies watching each other, and very anxious -to get together, while, however, they are separated from one another -by means of an insurmountable obstacle. They will thus remain facing -each other, and at their posts, while each side is, meanwhile, being -recruited by the same operation as before. We may by this means -accumulate a vast quantity of opposite electricities on the two -coatings of such a jar, and they will remain there for a long time, -especially if the surrounding atmosphere and the glass surface of the -jar be quite dry. When, however, electric connection of any kind is -made between the two coatings, the electricities rush together and -unite with one another in the shape of a spark, while if the human body -be the instrument of connecting them a severe shock will be felt. - -90. It would thus appear that, when two bodies charged with opposite -electricities are brought near each other, the two electricities rush -together, forming a current, and the ultimate result is a spark. -Now, this spark implies heat, and is, in truth, nothing else than -small particles of intensely heated matter of some kind. We have here, -therefore, first of all, the conversion of electrical separation into a -current of electricity, and, secondly, the conversion of this current -into heat. In this case, however, the current lasts only a very small -time; the discharge, as it is called, of a Leyden jar being probably -accomplished in ¹⁄₂₄₀₀₀th of a second. - - -_The Electric Current._ - -91. In other cases we have electrical currents which, although not so -powerful as that produced by discharging a Leyden jar, yet last longer, -and are, in fact, continuous instead of momentary. - -We may see a similar difference in the case of visible energy. Thus we -might, by means of gunpowder, send up in a moment an enormous mass of -water; or we might, by means of a fountain, send up the same mass in -the course of time, and in a very much quieter manner. We have the same -sort of difference in electrical discharges, and having spoken of the -rushing together of two opposite electricities by means of an explosion -and a spark, let us now speak of the eminently quiet and effective -_voltaic current_, in which we have a continuous coming together of the -same two agents. - -[Illustration: Fig. 8.] - -92. It is not our object here to give a complete description, either -historical or scientific, of the voltaic battery, but rather to give -such an account as will enable our readers to understand what the -arrangement is, and what sort of effect it produces; and with this -object we shall at once proceed to describe the battery of Grove, which -is perhaps the most efficacious of all the various arrangements for the -purpose of producing an electric current. In this battery we have a -number of cells connected together, as in Fig. 8, which shows a battery -of three cells. Each cell consists of two vessels, an outer and an -inner one; the outer vessel being made of glass or ordinary stone ware, -while the inner one is made of unglazed porcelain, and is therefore -porous. The outer vessel is filled with dilute sulphuric acid, and a -plate of amalgamated zinc--that is to say, of metallic zinc having -its outer surface brightened with mercury,--is immersed in this acid. -Again, in the inner or porous vessel we have strong nitric acid, in -which a plate of platinum foil is immersed, this being at the same time -electrically connected with the zinc plate of the next outer vessel, -by means of a clamp, as in the figure. Both metals must be clean where -they are pressed together, that is to say, the true metallic surfaces -of both must be in contact. Finally, a wire is metallically connected -with the platinum of the left-hand cell, and a similar wire with the -zinc of the right-hand cell, and these connecting wires ought, except -at their extremities, to be covered over with gutta-percha or thread. -The loose extremities of these wires are called the _poles_ of the -battery. - -93. Let us now suppose that we have a battery containing a good many -cells of this description, and let the whole arrangement be insulated, -by being set upon glass supports, or otherwise separated from the -earth. If now we test, by appropriate methods, the extremity of the -wire connected with the left-hand platinum plate, it will be found to -be charged with positive electricity, while the extremity of the other -wire will be found charged with negative electricity. - -94. In the next place, if we connect these poles of the battery with -one another, the two electricities will rush together and unite, or, -in other words, there will be an electric current; but it will not be -a momentary but a continuous one, and for some time, provided these -poles are kept together, a current of electricity will pass through the -wires, and indeed through the whole arrangement, including the cells. - -The direction of the current will be such that _positive electricity -may be supposed to pass from the zinc to the platinum, through the -liquid; and back again through the wire, from the platinum at the -left hand, to the zinc at the right_; in fact, to go in the direction -indicated by the arrow-head. - -95. Thus we have two things. In the first place, before the two -terminals, or poles, have been brought together, we have them charged -with opposite electricities; and, secondly, when once they have been -brought together, we have the production of a continuous current of -electricity. Now, this current is an energetic agent, in proof of which -we shall proceed to consider the various properties which it has,--the -various things which it can do. - - -_Its Magnetic Effects._ - -96. In the first place, _it can deflect the magnetic needle_. For -instance, let a compass needle be swung freely, and let a current of -electricity circulate along a wire placed near this needle, and in the -direction of its length, then the direction in which the needle points -will be immediately altered. This direction will now depend upon that -of the current, conveyed by the wire, and the needle will endeavour to -place itself at right angles to this wire. - -In order to remember the connection between the direction of the -current and that of the magnet, imagine your body to form part of the -positive current, which may be supposed to enter in at your head, and -go out at your feet; also imagine that your face is turned towards -the magnet. In this case, the pole of the magnet, which points to the -north, will always be deflected by the current towards your right -hand. The strength of a current may be measured by the amount of the -deflection it produces upon a magnetic needle, and the instrument by -which this measurement is made is called a _galvanometer_. - -97. In the next place, _the current is able_, not merely to deflect -a magnet, but also _to render soft iron magnetic_. Let us take, for -instance, the wire connected with the one pole of the battery, and -cover it with thread, in order to insulate it, and let us wrap this -wire round a cylinder of soft iron, as in Fig. 9. If we now make a -communication between the other extremity of the wire, and the other -pole of the battery, so as to make the current pass, it will be found -that our cylinder of soft iron has become a powerful magnet, and that -if an iron keeper be attached to it as in the figure, the keeper will -be able to sustain a very great weight. - -[Illustration: Fig. 9.] - - -_Its Heating Effect._ - -98. _The electric current has likewise the property of heating a wire -through which it passes._ To prove this, let us connect the two poles -of a battery by means of a fine platinum wire, when it will be found -that the wire will, in a few seconds, become heated to redness. In -point of fact, the current will heat a thick wire, but not so much as a -thin one, for we may suppose it to rush with great violence through the -limited section of the thin wire, producing in its passage great heat. - - -_Its Chemical Effect._ - -99. Besides its magnetic and heating effects, _the current has also the -power of decomposing compound substances_, under certain conditions. -Suppose, for instance, that the poles of a battery, instead of being -brought together, are plunged into a vessel of water, decomposition -will at once begin, and small bubbles of oxygen will rise from the -positive pole, while small bubbles of hydrogen will make their -appearance at the negative. If the two gases are collected together in -a vessel, they may be exploded, and if collected separately, it may -be proved by the ordinary tests, that the one is oxygen and the other -hydrogen. - - -_Attraction and Repulsion of Currents._ - -100. We have now described very shortly the magnetic, the heating, and -the chemical effects of currents; it remains for us to describe the -effects of currents upon one another. - -In the first place, suppose that we have two wires which are parallel -to one another, and carry currents going in the same direction; and -let us further suppose that these wires are capable of moving, then it -is found that they will attract one another. If, however, the wires, -although parallel, convey currents going in opposite directions, they -will then repel one another. A good way of showing this experimentally -is to cause two circular currents to float on water. If these currents -both go either in the same direction as the hands of a watch, or in -the opposite direction, then the two will attract one another; but if -the one goes in the one direction, and the other in the other, they -will then repel one another. - - -_Attraction and Repulsion of Magnets._ - -101. Ampère, who discovered this property of currents, has likewise -shown us that in very many respects a magnet may be likened to a -collection of circular currents all parallel to one another, their -direction being such that, if you look towards the north pole of a -freely suspended cylindrical magnet facing it, the positive current -will descend on the east or left-hand side, and ascend on the west or -right-hand side. If we adopt this method of viewing magnets, we can -easily account for the attraction between the unlike and the repulsion -between the like poles of a magnet, for when unlike poles are placed -near each other, the circular currents which face each other are then -all going in the same direction, and the two will, therefore, attract -one another, but if like poles are placed in this position, the -currents that face each other are going in opposite directions, and the -poles will, therefore, repel one another. - -[Illustration: Fig. 10.] - -_Induction of Currents._ - -102. Before closing this short sketch of electrical phenomena, we must -allude to the inductive effect of currents upon each other. Let us -suppose (Fig. 10) that we have two circular coils of wire, covered with -thread, and placed near each other. Let both the extremities of the -right-hand coil be connected with the poles of a battery, so as to make -a current of electricity circulate round the coil. On the other hand, -let the left-hand coil be connected with a galvanometer, thus enabling -us to detect the smallest current of electricity which may pass through -this coil. Now, it is found that when we first connect the right-hand -coil, so as to pass the battery current through it, a momentary current -will pass through the left-hand coil, and will deflect the needle of -the galvanometer, but this current will go in an opposite direction to -that which circulates round the right-hand coil. - -103. Again, as long as the current continues to flow through the -right-hand coil there will be no current through the other, but at -the moment of breaking the contact between the right-hand coil and -the battery there will again be a momentary current in the left-hand -coil, but this time in the same direction as that of the right-hand -coil, instead of being, as before, in the opposite direction. In other -words, when contact is _made_ in the right-hand coil, there is a -momentary current in the left-hand coil, but in an opposite direction -to that in the right, while, when contact is _broken_ in the right-hand -coil, there is a momentary current in the left-hand coil in the same -direction as that in the right. - -104. In order to exemplify this induction of currents, it is not even -necessary to make and break the current in the right-hand coil, for we -may keep it constantly going and arrange so as to make the right-hand -coil (always retaining its connection with the battery) alternately -approach and recede from the other; when it approaches the other, the -effect produced will be the same as when the contact was made in the -above experiment--that is to say, we shall have an induced current in -an opposite direction to that of the primary, while, when it recedes -from the other, we shall have a current in the same direction as that -of the primary. - -105. Thus we see that whether we keep both coils stationary, and -suddenly produce a current in the right-hand coil, or whether, keeping -this current constantly going, we suddenly bring it near the other -coil, the inductive effect will be precisely the same, for in both -cases the left-hand coil is suddenly brought into the presence of a -current. And again, it is the same, whether we suddenly break the -right-hand current, or suddenly remove it from the left-hand coil, for -in both cases this coil is virtually removed from the presence of a -current. - - -_List of Energies._ - -106. We are now in a position to enumerate the various kinds of -energy which occur in nature; but, before doing so, we must warn our -readers that this enumeration has nothing absolute or complete about -it, representing, as it does, not so much the present state of our -knowledge as of our want of knowledge, or rather profound ignorance, of -the ultimate constitution of matter. It is, in truth, only a convenient -classification, and nothing more. - -107. To begin, then, with visible energy. We have first of all-- - - -_Energy of Visible Motion._ - - (A.) Visible energy of actual motion--in the planets, in meteors, in - the cannon ball, in the storm, in the running stream, and in other - instances of bodies in actual visible motion, too numerous to be - mentioned. - - -_Visible Energy of Position._ - - (B.) We have also visible energy of position--in a stone on the top of - a cliff, in a head of water, in a rain cloud, in a cross-bow bent, in - a clock or watch wound up, and in various other instances. - -108. Then we have, besides, several cases in which there is an -alternation between (A) and (B). - -A pendulum, for instance, when at its lowest point, has only the -energy (A), or that of actual motion, in virtue of which it ascends a -certain distance against the force of gravity. When, however, it has -completed its ascent, its energy is then of the variety (B), being -due to position, and not to actual motion; and so on it continues to -oscillate, alternately changing the nature of its energy from (A) to -(B), and from (B) back again to (A). - -109. A vibrating body is another instance of this alternation. Each -particle of such a body may be compared to an exceedingly small -pendulum oscillating backwards and forwards, only very much quicker -than an ordinary pendulum; and just as the ordinary pendulum in passing -its point of rest has its energy all of one kind, while in passing its -upper point it has it all of another, so when a vibrating particle is -passing its point of rest, its energy is all of the variety (A), and -when it has reached its extreme displacement, it is all of the variety -(B). - - -_Heat Motion._ - - 110. (C.) Coming now to molecular or invisible energy, we have, in - the first place, that motion of the molecules of bodies which we term - heat. A better term would be _absorbed heat_, to distinguish it from - _radiant heat_, which is a very different thing. That peculiar motion - which is imparted by heat when absorbed into a body is, therefore, one - variety of molecular energy. - - -_Molecular Separation._ - - (D.) Analogous to this is that effect of heat which represents - position rather than actual motion. For part of the energy of absorbed - heat is spent in pulling asunder the molecules of the body under the - attractive force which binds them together (Art. 73), and thus a store - of energy of position is laid up, which disappears again after the - body is cooled. - - -_Atomic or Chemical Separation._ - - 111. (E.) The two previous varieties of energy may be viewed as - associated with molecules rather than with atoms, and with the force - of cohesion rather than with that of chemical affinity. Proceeding now - to atomic force, we have a species of energy of position due to the - separation of different atoms under the strong chemical attraction - they have for one another. Thus, when we possess coal or carbon and - also oxygen in a state of separation from one another, we are in - possession of a source of energy which may be called that of chemical - separation. - - -_Electrical Separation._ - - 112 (F.) The attraction which heterogeneous atoms possess for one - another, sometimes, however, gives rise to a species of energy which - manifests itself in a very peculiar form, and appears as electrical - separation, which is thus another form of energy of position. - - -_Electricity in Motion._ - - 113 (G.) But we have another species of energy connected with - electricity, for we have that due to electricity in motion, or in - other words, an electric current which probably represents some form - of actual motion. - - -_Radiant Energy._ - - 114 (H.) It is well known that there is no ordinary matter, or at - least hardly any, between the sun and the earth, and yet we have a - kind of energy which we may call radiant energy, which proceeds - to us from the sun, and proceeds also with a definite, though very - great velocity, taking about eight minutes to perform its journey. - Now, this radiant energy is known to consist of the vibrations of an - elastic medium pervading all space, which is called ether, or the - _ethereal medium_. Inasmuch, therefore, as it consists of vibrations, - it partakes of the character of pendulum motion, that is to say, the - energy of any ethereal particle is alternately that of position and - that of actual motion. - - -_Law of Conservation._ - -115. Having thus endeavoured, provisionally at least, to catalogue our -various energies, we are in a position to state more definitely what -is meant by the conservation of energy. For this purpose, let us take -the universe as a whole, or, if this be too large, let us conceive, if -possible, a small portion of it to be isolated from the rest, as far as -force or energy is concerned, forming a sort of microcosm, to which we -may conveniently direct our attention. - -This portion, then, neither parts with any of its energy to the -universe beyond, nor receives any from it. Such an isolation is, of -course, unnatural and impossible, but it is conceivable, and will, -at least, tend to concentrate our thoughts. Now, whether we regard -the great universe, or this small microcosm, the principle of the -conservation of energy asserts that the sum of all the various energies -is a constant quantity, that is to say, adopting the language of -Algebra-- - - (A) + (B) + (C) + (D) + (E) + (F) + (G) + (H) = a constant quantity. - -116. This does not mean, of course, that (A) is constant in itself, or -any other of the left-hand members of this equation, for, in truth, -they are always changing about into each other--now, some visible -energy being changed into heat or electricity; and, anon, some heat or -electricity being changed back again into visible energy--but it only -means that the sum of all the energies taken together is constant. We -have, in fact, in the left hand, eight variable quantities, and we -only assert that their sum is constant, not by any means that they are -constant themselves. - -117. Now, what evidence have we for this assertion? It may be replied -that we have the strongest possible evidence which the nature of the -case admits of. The assertion is, in truth, a peculiar one--peculiar -in its magnitude, in its universality, in the subtle nature of the -agents with which it deals. If true, its truth certainly cannot be -proved after the manner in which we prove a proposition in Euclid. -Nor does it even admit of a proof so rigid as that of the somewhat -analogous principle of the conservation of matter, for in chemistry we -may confine the products of our chemical combination so completely -as to prove, beyond a doubt, that no heavy matter passes out of -existence that--when coal, for instance, burns in oxygen gas--what we -have is merely a change of condition. But we cannot so easily prove -that no energy is destroyed in this combination, and that the only -result is a change from the energy of chemical separation into that of -absorbed heat, for during the process it is impossible to isolate the -energy--do what we may, some of it will escape into the room in which -we perform the experiment; some of it will, no doubt, escape through -the window, while a little will leave the earth altogether, and go -out into space. All that we can do in such a case is to estimate, as -completely as possible, how much energy has gone away, since we cannot -possibly prevent its going. But this is an operation involving great -acquaintance with the laws of energy, and very great exactness of -observation: in fine, our readers will at once perceive that it is much -more difficult to prove the truth of the conservation of energy than -that of the conservation of matter. - -118. But if it be difficult to prove our principle in the most rigorous -manner, we are yet able to give the strongest possible indirect -evidence of its truth. - -Our readers are no doubt familiar with a method which Euclid frequently -adopts in proving his propositions. Starting with the supposition -that they are not true, and reasoning upon this hypothesis, he comes -to an absurd conclusion--hence he concludes that they are true. Now, -we may adopt a method somewhat similar with regard to our principle, -only instead of supposing it untrue, let us suppose it true. It may -then be shown that, if it be true, under certain test conditions we -ought to obtain certain results--for instance, if we increase the -pressure, we ought to lower the freezing point of water. Well, we make -the experiment, and find that, in point of fact, the freezing point of -water is lowered by increasing the pressure, and we have thus derived -an argument in favour of the conservation of energy. - -119. Or again, if the laws of energy are true, it may be shown that, -whenever a substance contracts when heated, it will become colder -instead of hotter by compression. Now, we know that ice-cold water, -or water just a little above its freezing point, contracts instead -of expanding up to 4° C.; and Sir William Thomson has found, by -experiment, that water at this temperature is cooled instead of heated -by sudden compression. India-rubber is another instance of this -relation between these two properties, for if we stretch a string of -india-rubber it gets hotter instead of colder, that is to say, its -temperature rises by extension, and gets lower by contraction; and -again, if we heat the string, we find that it contracts in length -instead of expanding like other substances as its temperature increases. - -120. Numberless instances occur in which we are enabled to predict -what will happen by assuming the truth of the laws of energy; in other -words, these laws are proved to be true in all cases where we can put -them to the test of rigorous experiment, and probably we can have no -better proof than this of the truth of such a principle. We shall -therefore proceed upon the assumption that the conservation of energy -holds true in all cases, and give our readers a list of the various -transmutations of this subtle agent as it goes backwards and forwards -from one abode to another, making, meanwhile, sundry remarks that may -tend, we trust, to convince our readers of the truth of our assumption. - - - - - - -CHAPTER IV. - -_TRANSMUTATIONS OF ENERGY._ - - -_Energy of Visible Motion._ - -121. Let us begin our list of transmutations with the energy of -visible motion. This is changed into _energy of position_ when a stone -is projected upwards above the earth, or, to take a case precisely -similar, when a planet or a comet goes from perihelion, or its position -nearest the sun, to aphelion, or its position furthest from the sun. -We thus see why a heavenly body should move fastest at perihelion, and -slowest at aphelion. If, however, a planet were to move round the sun -in an orbit exactly circular, its velocity would be the same at all the -various points of this orbit, because there would be no change in its -distance from the centre of attraction, and therefore no transmutation -of energy. - -122. We have already (Arts. 108, 109) said that the energy in an -oscillating or vibrating body is alternately that of actual motion, and -that of position. In this respect, therefore, a pendulum is similar to -a comet or heavenly body with an elliptical orbit. Nevertheless the -change of energy is generally more complete in a pendulum or vibrating -body than it is in a heavenly body; for in a pendulum, when at its -lowest point, the energy is entirely that of actual motion, while at -its upper point it is entirely that of position. Now, in a heavenly -body we have only a lessening, but not an entire destruction, of the -velocity, as the body passes from perihelion to aphelion--that is to -say, we have only a partial conversion of the one kind of energy into -the other. - -123. Let us next consider the change of actual visible energy into -_absorbed heat_. This takes place in all cases of friction, percussion, -and resistance. In friction, for instance, we have the conversion of -work or energy into heat, which is here produced through the rubbing -of surfaces against each other; and Davy has shown that two pieces of -ice, both colder than the freezing point, may be melted by friction. -In percussion, again, we have the energy of the blow converted into -heat; while, in the case of a meteor or cannon ball passing through the -air with great velocity, we have the loss of energy of the meteor or -cannon ball through its contact with the air, and at the same time the -production of heat on account of this resistance. - -The resistance need not be atmospheric, for we may set the cannon ball -to pierce through wooden planks or through sand, and there will equally -be a production of heat on account of the resistance offered by the -wooden planks or by the sand to the motion of the ball. We may even -generalize still further, and assert that whenever the visible momentum -of a body is transferred to a larger mass, there is at the same time -the conversion of visible energy into heat. - -124. A little explanation will be required to make this point clear. - -The third law of motion tells us that action and reaction are equal and -opposite, so that when two bodies come into collision the forces at -work generate equal and opposite quantities of momentum. We shall best -see the meaning of this law by a numerical example, bearing in mind -that momentum means the product of mass into velocity. - -For instance, let us suppose that an inelastic body of mass 10 and -velocity 20 strikes directly another inelastic body of mass 15 and -velocity 15, the direction of both motions being the same. - -Now, it is well known that the united mass will, after impact, be -moving with the velocity 17. What, then, has been the influence of the -forces developed by collision? The body of greater velocity had before -impact a momentum 10 × 20 = 200, while its momentum after impact is -only 10 × 17 = 170; it has therefore suffered a loss of 30 units as -regards momentum, or we may consider that a momentum of 30 units has -been impressed upon it in an opposite direction to its previous motion. - -On the other hand, the body of smaller velocity had before impact a -momentum 15 × 15 = 225, while after impact it has 15 × 17 = 255 units, -so that its momentum has been increased by 30 units in its previous -direction. - -The force of impact has therefore generated 30 units of momentum in two -opposite directions, so that, taking account of direction, the momentum -of the system is the same before and after impact; for before impact we -had a momentum of 10 × 20 + 15 × 15 = 425, while after it we have the -united mass 25 moving with the velocity 17, giving the momentum 425 as -before. - -125. But while the momentum is the same before and after impact, the -visible energy of the moving mass is undoubtedly less after impact -than before it. To see this we have only to turn to the expression -of Art. 28, from which we find that the energy before impact was as -follows:--Energy in kilogrammetres = (_m v_²)/(19 · 6) = (10 × 20² + 15 -× 15²)/19·6 = 376 nearly; while that after impact = (25 × 17²)/19·6 = -368 nearly. - -126. The loss of energy will be still more manifest if we suppose an -inelastic body in motion to strike against a similar body at rest. Thus -if we have a body of mass 20 and velocity 20 striking against one of -equal mass, but at rest, the velocity of the double mass after impact -will obviously be only 10; but, as regards energy, that before impact -will be (20 × 20²)/19·6 = ⁸⁰⁰⁰⁄₁₉·6 while that after impact will be -(40 × 10²)/19·6 = ⁴⁰⁰⁰⁄₁₉·6 or only half the former. - -127. Thus there is in all such cases an apparent loss of visible -energy, while at the same time there is the production of heat on -account of the blow which takes place. If, however, the substances that -come together be perfectly elastic (which no substance is), the visible -energy after impact will be the same as that before, and in this case -there will be no conversion into heat. This, however, is an extreme -supposition, and inasmuch as no substance is perfectly elastic, we -have in all cases of collision a greater or less conversion of visible -motion into heat. - -128. We have spoken (Art. 122) about the change of energy in an -oscillating or vibrating body, as if it were entirely one of actual -energy into energy of position, and the reverse. - -But even here, in each oscillation or vibration, there is a greater -or less conversion of visible energy into heat. Let us, for instance, -take a pendulum, and, in order to make the circumstances as favourable -as possible, let it swing on a knife edge, and in vacuo; in this case -there will be a slight but constant friction of the knife edge against -the plane on which it rests, and though the pendulum may continue to -swing for hours, yet it will ultimately come to rest. - -And, again, it is impossible to make a vacuum so perfect that there is -absolutely no air surrounding the pendulum, so that part of the motion -of the pendulum will always be carried off by the residual air of the -vacuum in which it swings. - -129. Now, something similar happens in that vibratory motion which -constitutes sound. Thus, when a bell is in vibration, part of the -energy of the vibration is carried off by the surrounding air, and it -is in virtue of this that we hear the sound of the bell; but, even if -there were no air, the bell would not go on vibrating for ever. For -there is in all bodies a greater or less amount of internal viscosity, -a property which prevents perfect freedom of vibration, and which -ultimately converts vibrations into heat. - -A vibrating bell is thus very much in the same position as an -oscillating pendulum, for in both part of the energy is given off to -the air, and in both there is unavoidable friction--in the one taking -the shape of internal viscosity, and in the other that of friction of -the knife edge against the plane on which it rests. - -130. In both these cases, too, that portion of the energy which goes -into the air takes ultimately the shape of heat. The oscillating -pendulum communicates a motion to the air, and this motion ultimately -heats the air. The vibrating bell, or musical instrument, in like -manner communicates part of its energy to the air. This communicated -energy first of all moves through the air with the well-known velocity -of sound, but during its progress it, too, no doubt becomes partly -converted into heat. Ultimately, it is transmitted by the air to other -bodies, and by means of their internal viscosity is sooner or later -converted into heat. Thus we see that heat is the form of energy, into -which all visible terrestrial motion, whether it be rectilinear, or -oscillatory, or vibratory, is ultimately changed. - -131. In the case of a body in visible rectilinear motion on the earth’s -surface, this change takes place very soon--if the motion be rotatory, -such as that of a heavy revolving top, it may, perhaps, continue longer -before it is ultimately stopped, by means of the surrounding air, and -by friction of the pivot; if it be oscillatory, as in the pendulum, or -vibratory, as in a musical instrument, we have seen that the air and -internal friction are at work, in one shape or another, to carry it -off, and will ultimately succeed in converting it into heat. - -132. But, it may be said, why consider a body moving on the earth’s -surface? why not consider the motion of the earth itself? Will this -also ultimately take the shape of heat? - -No doubt it is more difficult to trace the conversion in such a case, -inasmuch as it is not proceeding at a sensible rate before our eyes. In -other words, the very conditions that make the earth habitable, and a -fit abode for intelligent beings like ourselves, are those which unfit -us to perceive this conversion of energy in the case of the earth. Yet -we are not without indications that it is actually taking place. For -the purpose of exhibiting these, we may divide the earth’s motion into -two--a motion of rotation, and one of revolution. - -133. Now, with regard to the earth’s rotation, the conversion of the -visible energy of this motion into heat is already well recognized. To -understand this we have only to study the nature of the moon’s action -upon the fluid portions of our globe. In the following diagram (Fig. -11) we have an exaggerated representation of this, by which we see that -the spherical earth is converted into an elongated oval, of which one -extremity always points to the moon. The solid body of the earth itself -revolves as usual, but, nevertheless, this fluid protuberance remains -always pointing towards the moon, as we see in the figure, and hence -the earth rubs against the protuberance as it revolves. The friction -produced by this action tends evidently to lessen the rotatory energy -of the earth--in other words, it acts like a break--and we have, just -as by a break-wheel, the conversion of visible energy into heat. This -was first recognized by Mayer and J. Thomson. - -[Illustration: Fig. 11.] - -134. But while there can be no doubt about the fact of such a -conversion going on, the only question is regarding its rate of -progress, and the time required before it can cause a perceptible -impression upon the rotative energy of the earth. - -Now, it is believed by astronomers that they have detected evidence of -such a change, for our knowledge of the motions of the sun and moon has -become so exact, that not only can we carry forward our calculations so -as to predict an eclipse, but also carry them backwards, and thus fix -the dates and even the very details of the ancient historical eclipses. - -If, however, between those times and the present, the earth has lost a -little rotative energy on account of this peculiar action of the moon, -then it is evident that the calculated circumstances of the ancient -total eclipse will not quite agree with those actually recorded; and by -a comparison of this nature it is believed that we have detected a very -slight falling off in the rotative energy of our earth. If we carry out -the argument, we shall be driven to the conclusion that the rotative -energy of our globe will, on account of the moon’s action, always get -less and less, until things are brought into such a state that the -rotation comes to be performed in the same time as the revolution of -the moon, so that then the same portion of the terrestrial surface -being always presented to the moon, it is evident that there will be no -effort made by the solid substance of the earth, to glide from under -the fluid protuberance, and there will in consequence be no friction, -and no further loss of energy. - -135. If the fate of the earth be ultimately to turn the same face -always to the moon, we have abundant evidence that this very fate has -long since overtaken the moon herself. Indeed, the much stronger effect -of our earth upon the moon has produced this result, probably, even in -those remote periods when the moon was chiefly fluid; and it is a fact -well known, not merely to astronomers, but to all of us, that the moon -nowadays turns always the same face to the earth.[4] No doubt this fate -has long since overtaken the satellites of Jupiter, Saturn, and the -other large planets; and there are independent indications that, at -least in the case of Jupiter, the satellites turn always the same face -to their primary. - -136. To come now to the energy of revolution of the earth, in her -orbit round the sun, we cannot help believing that there is a material -medium of some kind between the sun and the earth; indeed, the -undulatory theory of light requires this belief. But if we believe in -such a medium, it is difficult to imagine that its presence will not -ultimately diminish the motion of revolution of the earth in her orbit; -indeed, there is a strong scientific probability, if not an absolute -certainty, that such will be the case. There is even some reason to -think that the energy of a comet of small period, called Encke’s -comet, is gradually being stopped from this cause; in fine, there can -be hardly any doubt that the cause is really in operation, and will -ultimately affect the motions of the planets and other heavenly bodies, -even although its rate of action may be so slow that we are not able to -detect it. - -We may perhaps generalize by saying, that wherever in the universe -there is a differential motion, that is to say, a motion of one part -of it towards or from another, then, in virtue of the subtle medium, -or cement, that binds the various parts of the universe together, this -motion is not unattended by something like friction, in virtue of which -the differential motion will ultimately disappear, while the loss of -energy caused by its disappearance will assume the form of heat. - -137. There are, indeed, obscure intimations that a conversion of this -kind is not improbably taking place in the solar system; for, in the -sun himself, we have the matter near the equator, by virtue of the -rotation of our luminary, carried alternately towards and from the -various planets. Now, it would seem that the sun-spots, or atmospheric -disturbances of the sun, affect particularly his equatorial regions, -and have likewise a tendency to attain their maximum size in that -position, which is as far away as possible from the influential -planets, such as Mercury or Venus;[5] so that if Venus, for instance, -were between the earth and the sun, there would be few sun-spots in the -middle of the sun’s disc, because that would be the part of the sun -nearest Venus. - -But if the planets influence sun-spots, the action is no doubt -reciprocal, and we have much reason to believe that sun-spots -influence, not only the magnetism, but also the meteorology of our -earth, so that there are most displays of the Aurora Borealis, as well -as most cyclones, in those years when there are most sun-spots.[6] Is -it not then possible that, in these strange, mysterious phenomena, we -see traces of the machinery by means of which the differential motion -of the solar system is gradually being changed into heat? - -138. We have thus seen that visible energy of actual motion is not -unfrequently changed into visible energy of position, and that it is -also very often transformed into absorbed heat. We have now to state -that it may likewise be transformed into _electrical separation_. -Thus, when an ordinary electrical machine is in action, considerable -labour is spent in turning the handle; it is, in truth, harder to turn -than if no electricity were being produced--in other words, part of -the energy which is spent upon the machine goes to the production of -electrical separation. There are other ways of generating electricity -besides the frictional method. If, for instance, we bring an insulated -conducting plate near the prime conductor of the electrical machine, -yet not near enough to cause a spark to pass, and if we then touch the -insulated plate, we shall find it, after contact, to be charged with an -electricity the opposite of that in the machine; we may then remove it -and make use of this electricity. - -It requires a little thought to see what labour we have spent in this -process. We must bear in mind that, by touching the plate, we have -carried off the electricity of the same name as that of the machine, -so that, after touching the insulated plate it is more strongly -attracted to the conductor than it was before. When we begin to remove -it, therefore, it will cost us an effort to do so, and the mechanical -energy which we spend in removing it will account for the energy of -electrical separation which we then obtain. - -139. We may thus make use of a small nucleus of electricity, to assist -us in procuring an unlimited supply, for in the above process the -electricity of the prime conductor remains unaltered, and we may repeat -the operation as often as we like, and gather together a very large -quantity of electricity, without finally altering the electricity of -the prime conductor, but not, however, without the expenditure of an -equivalent amount of energy, in the shape of actual work. - -140. While, as we have seen, there is a tendency in all motion to be -changed into heat, there is one instance where it is, in the first -place at least, changed into _a current of electricity_. We allude -to the case where a conducting substance moves in the presence of an -electric current, or of a magnet. - -In Art. 104 we found that if one coil connected with a battery were -quickly moved into the presence of another coil connected with a -galvanometer, an induced current would be generated in the latter coil, -and would affect the galvanometer, its direction being the reverse of -that passing in the other. Now, an electric current implies energy, and -we may therefore conclude that some other form of energy must be spent, -or disappear, in order to produce the current which is generated in the -coil attached to the galvanometer. - -Again, we learn from Art. 100 that two currents going in opposite -directions repel one another. The current generated in the coil -attached to the galvanometer or secondary current will, therefore, -repel the primary current, which is moving towards it; this repulsion -will either cause a stoppage of motion, or render necessary the -expenditure of energy, in order to keep up the motion of this moving -coil. We thus find that two phenomena occur simultaneously. In the -first place, there is the production of energy in the secondary coil, -in the shape of a current opposite in direction to that of the primary -coil; in the next case, owing to the repulsion between this induced -current and the primary current, there is a stoppage or disappearance -of the energy of actual motion of the moving coil. We have, in fact, -the creation of one species of energy, and at the same time the -disappearance of another, and thus we see that the law of conservation -is by no means broken. - -141. We see also the necessary connection between the two electrical -laws described in Arts. 100 and 104. Indeed, had these laws been other -than what they are, the principle of conservation of energy would have -been broken. - -For instance, had the induced current in the case now mentioned been -in the same direction as that of the primary, the two currents would -have attracted each other, and thus there would have been the creation -of a secondary current, implying energy, in the coil attached to the -galvanometer, along with an increase of the visible energy of motion -of the primary current--that is to say, instead of the creation of -one kind of energy, accompanied with the disappearance of another, we -should have had the simultaneous creation of both; and thus the law of -conservation of energy would have been broken. - -We thus see that the principle of conservation enables us to deduce -the one electrical law from the other, and this is one of the many -instances which strengthen our belief in the truth of the great -principle for which we are contending. - -142. Let us next consider what will take place if we cause the primary -current to move from the secondary coil instead of towards it. - -In this case we know, from Art. 104, that the induced current will be -in the same direction as the primary, while we are told by Art. 100 -that the two currents will now attract each other. The tendency of this -attraction will be to stop the motion of the primary current from -the secondary one, or, in other words, there will be a disappearance -of the energy of visible motion, while at the same time there is the -production of a current. In both cases, therefore, one form of energy -disappears while another takes its place, and in both there will be a -very perceptible resistance experienced in moving the primary coil, -whether towards the secondary or from it. Work will, in fact, have to -be spent in both operations, and the outcome of this work or energy -will be the production of a current in the first place, and of heat in -the second; for we learn from Art. 98 that when a current passes along -a wire its energy is generally spent in heating the wire. - -We have thus two phenomena occurring together. In the first place, in -moving a current of electricity to and from a coil of wire, or any -other conductor, or (which is the same thing, since action and reaction -are equal and opposite) in moving a coil of wire or any other conductor -to and from a current of electricity, a sense of resistance will be -experienced, and energy will have to be spent upon the process; in the -second place, an electrical current will be generated in the conductor, -and the conductor will be heated in consequence. - -143. The result will be rendered very prominent if we cause a metallic -top, in rapid rotation, to spin near two iron poles, which, by means -of the battery, we can suddenly convert into the poles of a powerful -electro-magnet. When this change is made, and the poles become -magnetic, the motion of the top is very speedily brought to rest, -just as if it had to encounter a species of invisible friction. This -curious result can easily be explained. We have seen from Art. 101 -that a magnet resembles an assemblage of electric currents, and in the -metallic top we have a conductor alternately approaching these currents -and receding from them; and hence, according to what has been said, we -shall have a series of secondary currents produced in the conducting -top which will stop its motion, and which will ultimately take the -shape of heat. In other words, the visible energy of the top will be -changed into heat just as truly as if it were stopped by ordinary -friction. - -144. The electricity induced in a metallic conductor, moved in -the presence of a powerful magnet, has received the name of -Magneto-Electricity; and Dr. Joule has made use of it as a convenient -means of enabling him to determine the mechanical equivalent of heat, -for it is into heat that the energy of motion of the conductor is -ultimately transformed. But, besides all this, these currents form, -perhaps, the very best means of obtaining electricity; and recently -very powerful machines have been constructed by Wild and others with -this view. - -145. These machines, when large, are worked by a steam-engine, and -their mode of operation is as follows:--The nucleus of the machine -is a system of powerful permanent steel magnets, and a conducting -coil is made to revolve rapidly in presence of these magnets. The -current produced by this moving coil is then used in order to produce -an extremely powerful electro-magnet, and finally a coil is made to -move with great rapidity in presence of this powerful electro-magnet, -thus causing induced currents of vast strength. So powerful are these -currents, that when used to produce the electric light, small print may -be read on a dark night at the distance of two miles from the scene of -operation! - -It thus appears that in this machine a double use is made of -magneto-electricity. Starting with a nucleus of permanent magnetism, -the magneto-electric currents are used, in the first instance, to -form a powerful electro-magnet much stronger than the first, and this -powerful electro-magnet is again made use of in the same way as the -first, in order to give, by means of magneto-electricity, an induced -current of very great strength. - -146. There is, moreover, a very great likeness between a -magneto-electric machine like that of Wild’s for generating electric -currents, and the one which generates statical electricity by means of -the method already described Art. 139. In both cases advantage is taken -of a nucleus, for in the magneto-electric machine we have the molecular -currents of a set of permanent magnets, which are made the means of -generating enormous electric currents without any permanent alteration -to themselves, yet not without the expenditure of work. - -Again, in an induction machine for generating statical electricity, -we have an electric nucleus, such as we have supposed to reside in the -prime conductor of a machine; and advantage may be taken, as we have -seen, of this nucleus in order to generate a vast quantity of statical -electricity, without any permanent alteration of the nucleus, but not -without the expenditure of work. - -147. We have now seen under what conditions the visible energy of -actual motion may be changed--1stly, into energy of position; 2ndly, -into the two energies which embrace absorbed heat; 3rdly, into -electrical separation; and finally into electricity in motion. As far -as we know, visible energy cannot directly be transformed into chemical -separation, or into radiant energy. - - -_Visible Energy of Position._ - -148. Having thus exhausted the transmutations of the energy of -visible motion, we next turn to that of position, and find that it -is transmuted into motion, but not immediately into any other form -of energy; we may, therefore, dismiss this variety at once from our -consideration. - - -_Absorbed Heat._ - -140. Coming now to these two forms of energy which embrace _absorbed -heat_, we find that this may be converted into (A) or _actual visible -energy_ in the case of the steam-engine, the air-engine, and all -varieties of heat engines. In the steam-engine, for instance, part -of the heat which passes through it disappears as heat, utterly and -absolutely, to reappear as mechanical effect. There is, however, one -condition which must be rigidly fulfilled, whenever heat is changed -into mechanical effect--there must be a difference of temperature, and -_heat will only be changed into work, while it passes from a body of -high temperature to one of low_. - -Carnot, the celebrated French physicist, has ingeniously likened the -mechanical power of heat to that of water; for just as you can get -no work out of heat unless there be a flow of heat from a higher -temperature level to a lower, so neither can you get work out of water -unless it be falling from a higher level to a lower. - -150. If we reflect that heat is essentially distributive in its nature, -we shall soon perceive the reason for this peculiar law; for, in virtue -of its nature, heat is always rushing from a body of high temperature -to one of low, and if left to itself it would distribute itself equally -amongst all bodies, so that they would ultimately become of the same -temperature. Now, if we are to coax work out of heat, we must humour -its nature, for it may be compared to a pack of schoolboys, who are -always ready to run with sufficient violence out of the schoolroom into -the open fields, but who have frequently to be dragged back with a very -considerable expenditure of energy. So heat will not allow itself to be -confined, but will resist any attempt to accumulate it into a limited -space. Work cannot, therefore, be gained by such an operation, but -must, on the contrary, be spent upon the process. - -151. Let us now for a moment consider the case of an enclosure in which -everything is of the same temperature. Here we have a dull dead level -of heat, out of which it will be impossible to obtain the faintest -semblance of work. The temperature may even be high, and there may be -immense stores of heat energy in the enclosure, but not a trace of this -is available in the shape of work. Taking up Carnot’s comparison, the -water has already fallen to the same level, and lies there without any -power of doing useful work--dead, in a sense, as far as visible energy -is concerned. - -152. We thus perceive that, firstly, we can get work out of heat when -it passes from a higher to a lower temperature, but that, secondly, -we must spend work upon it in order to make it pass from a lower -temperature to a higher one; and that, thirdly and finally, nothing -in the shape of work can be got out of heat which is all at the same -temperature level. - -What we have now said enables us to realize the conditions under which -all heat engines work. The essential point about such engines is, not -the possession of a cylinder, or piston, or fly wheels, or valves, -but the possession of two chambers, one of high and the other of low -temperature, while it performs work in the process of carrying heat -from the chamber of high to that of low temperature. - -Let us take, for example, the low-pressure engine. Here we have the -boiler or chamber of high, and the condenser or chamber of low, -temperature, and the engine works while heat is being carried from -the boiler to the condenser--never while it is being carried from the -condenser to the boiler. - -In like manner in the locomotive we have the steam generated at a high -temperature and pressure, and cooled by injection into the atmosphere. - -153. But, leaving formal engines, let us take an ordinary fire, which -plays in truth the part of an engine, as far as energy is concerned. -We have here the cold air streaming in over the floor of the room, -and rushing into the fire, to be there united with carbon, while -the rarefied product is carried up the chimney. Dismissing from our -thoughts at present the process of combustion, except as a means of -supplying heat, we see that there is a continual in-draught of cold -air, which is heated by the fire, and then sent to mingle with the -air above. Heat is, in fact, distributed by this means, or carried -from a body of high temperature, _i.e._ the fire, to a body of low -temperature, _i.e._ the outer air, and in this process of distribution -mechanical effect is obtained in the up-rush of air through the chimney -with considerable velocity. - -154. Our own earth is another instance of such an engine, having -the equatorial regions as its boiler, and the polar regions as its -condensers; for, at the equator, the air is heated by the direct -rays of the sun, and we have there an ascending current of air, up a -chimney as it were, the place of which is supplied by an in-draught of -colder air along the ground or floor of the world, from the poles on -both sides. Thus the heated air makes its way from the equator to the -poles in the upper regions of the atmosphere, while the cold air makes -its way from the poles to the equator along the lower regions. Very -often, too, aqueous vapour as well as air is carried up by means of -the sun’s heat to the upper and colder atmospheric regions, and there -deposited in the shape of rain, or hail, or snow, which ultimately -finds its way back again to the earth, often displaying in its passage -immense mechanical energy. Indeed, the mariner who hoists his sail, -and the miller who grinds his corn (whether he use the force of the -wind or that of running water), are both dependent upon this great -earth-engine, which is constantly at work producing mechanical effect, -but always in the act of carrying heat from its hotter to its colder -regions. - -155. Now, if it be essential to an engine to have two chambers, one -hot and one cold, it is equally important that there should be a -considerable temperature difference between the two. - -If Nature insists upon a difference before she will give us work, we -shall not be able to pacify her, or to meet her requirements by making -this difference as small as possible. And hence, _cæteris paribus_, we -shall obtain a greater proportion of work out of a certain amount of -heat passing through our engine when the temperature difference between -its boiler and condenser is as great as possible. In a steam-engine -this difference cannot be very great, because if the water of the -boiler were at a very high temperature the pressure of its steam would -become dangerous; but in an air-engine, or engine that heats and -cools air, the temperature difference may be much larger. There are, -however, practical inconveniences in engines for which the temperature -of the boiler is very high, and it is possible that these may prove -so formidable as to turn the scale against such engines, although in -theory they ought to be very economical. - -156. The principles now stated have been employed by Professor J. -Thomson, in his suggestion that the application of pressure would be -found to lower the freezing point of water; and the truth of this -suggestion was afterwards proved by Professor Sir W. Thomson. The -following was the reasoning employed by the former:-- - -Suppose that we have a chamber kept constantly at the temperature 0° -C., or the melting point of ice, and that we have a cylinder, of which -the sectional area is one square metre, filled one metre in height with -water, that is to say, containing one cubic metre of water. Suppose, -next, that a well-fitting piston is placed above the surface of the -water in this cylinder, and that a considerable weight is placed upon -the piston. Let us now take the cylinder, water and all, and carry it -into another room, of which the temperature is just a trifle lower. In -course of time the water will freeze, and, as it expands in freezing, -it will push up the piston and weight about ⁹⁄₁₀₀ths of a metre; and we -may suppose that the piston is kept fastened in this position by means -of a peg. Now carry back the machine into the first room, and in the -course of time the ice will be melted, and we shall have water once -more in the cylinder, but there will now be a void space of ⁹⁄₁₀₀ths -of a metre between the piston and the surface. We have thus acquired -a certain amount of energy of position, and we have only to pull out -the peg, and allow the piston with its weight to fall down through -the vacant space, in order to utilize this energy, after which the -arrangement is ready to start afresh. Again, if the weight be very -great, the energy thus gained will be very great; in fact, the energy -will vary with the weight. In fine, the arrangement now described is -a veritable heat engine, of which the chamber at 0° C. corresponds to -the boiler, and the other chamber a trifle lower in temperature to -the condenser, while the amount of work we get out of the engine--or, -in other words, its efficiency--will depend upon the weight which is -raised through the space of ⁹⁄₁₀₀ths of a metre, so that, by increasing -this weight without limit, we may increase the efficiency of our engine -without limit. It would thus at first sight appear that by this device -of having two chambers, one at 0° C., and the other a trifle lower, -we can get any amount of work out of our water engine; and that, -consequently, we have managed to overcome Nature. But here Thomson’s -law come into operation, showing that we cannot overcome Nature by any -such device, but that if we have a large weight upon our piston, we -must have a proportionally large difference of temperature between our -two chambers--that is to say, the freezing point of water, under great -pressure, will be lower in temperature than its freezing point, if the -pressure upon it be only small. - -Before leaving this subject we must call upon our readers to realize -what takes place in all heat engines. It is not merely that heat -produces mechanical effect, but that _a given quantity of heat -absolutely passes out of existence as heat in producing its equivalent -of work_. If, therefore, we could measure the mere heat produced in an -engine by the burning of a ton of coals, we should find it to be less -when the engine was doing work than when it was at rest. - -In like manner, when a gas expands suddenly its temperature falls, -because a certain amount of its heat passes out of existence in the act -of producing mechanical effect. - -157. We have thus endeavoured to show under what conditions absorbed -heat may be converted into mechanical effect. This absorbed heat -embraces (Art. 110) two varieties of energy, one of these being -molecular motion, and the other molecular energy of position. - -Let us now, therefore, endeavour to ascertain under what circumstances -the one of these varieties may be changed into the other. It is well -known that it takes a good deal of heat to convert a kilogramme of ice -into water, and that when the ice is melted the temperature of the -water is not perceptibly higher than that of the ice. It is equally -well known that it takes a great deal of heat to convert a kilogramme -of boiling water into steam, and that when the transformation is -accomplished, the steam produced is not perceptibly hotter than the -boiling water. In such cases the heat is said to become latent. - -Now, in both these cases, but more obviously in the last, we may -suppose that the heat has not had its usual office to perform, but -that, instead of increasing the motion of the molecules of water, it -has spent its energy in tearing them asunder from each other, against -the force of cohesion which binds them together. - -Indeed, we know as a matter of fact that the force of cohesion which is -perceptible in boiling water is apparently absent from steam, or the -vapour of water, because its molecules are too remote from one another -to allow of this force being appreciable. We may, therefore, suppose -that a large part, at least, of the heat necessary to convert boiling -water into steam is spent in doing work against molecular forces. - -When the steam is once more condensed into hot water, the heat thus -spent reassumes the form of molecular motion, and the consequence -is that we require to take away somehow all the latent heat of a -kilogramme of steam before we can convert it into boiling water. In -fact, if it is difficult and tedious to convert water into steam, it is -difficult and tedious to convert steam into water. - -158. Besides the case now mentioned, there are other instances in -which, no doubt, molecular separation becomes gradually changed into -heat motion. Thus, when a piece of glass has been suddenly cooled, -its particles have not had time to acquire their proper position, and -the consequence is that the whole structure is thrown into a state of -constraint. In the course of time such bodies tend to assume a more -stable state, and their particles gradually come closer together. - -It is owing to this cause that the bulb of a thermometer recently blown -gradually contracts, and it is no doubt owing to the same cause that a -Prince Rupert’s drop, formed by dropping melted glass into water, when -broken, falls into powder with a kind of explosion. It seems probable -that in all such cases these changes are attended with heat, and that -they denote the conversion of the energy of molecular separation into -that of molecular motion. - -159. Having thus examined the transmutations of (C) into (D), and -of (D) back again into (C), let us now proceed with our list, and -see under what circumstances absorbed heat is changed into _chemical -separation_. - -It is well known that when certain bodies are heated, they are -decomposed; for instance, if limestone or carbonate of lime be heated, -it is decomposed, the carbonic acid being given out in the shape of -gas, while quick-lime remains behind. Now, heat is consumed in this -process, that is to say, a certain amount of heat energy absolutely -passes out of existence _as heat_ and is changed into the energy of -chemical separation. Again, if the lime so obtained be exposed, under -certain circumstances, to an atmosphere of carbonic acid, it will -gradually become changed into carbonate of lime; and in this change -(which is a gradual one) we may feel assured that the energy of -chemical separation is once more converted into the energy of heat, -although we may not perceive any increment of temperature, on account -of the slow nature of the process. - -At very high temperatures it is possible that most compounds are -decomposed, and the temperature at which this takes place, for any -compound, has been termed its _temperature of disassociation_. - -160. Heat energy is changed into _electrical separation_ when -tourmalines and certain other crystals are heated. - -Let us take, for instance, a crystal of tourmaline and raise its -temperature, and we shall find one end positively, and the other -negatively, electrified. Again, let us take the same crystal, and -suddenly cool it, and we shall find an electrification of the -opposite kind to the former, so that the end of the axis, which -was then positive, will now be negative. Now, this separation of -the electricities denotes energy; and we have, therefore, in such -crystals a case where the energy of heat has been changed into that -of electrical separation. In other words, a certain amount of heat has -passed out of existence _as heat_, while in its place a certain amount -of electrical separation has been obtained. - -161. Let us next see under what circumstances heat is changed -into _electricity in motion_. This transmutation takes place in -thermo-electricity. - -Suppose, for instance, that we have a bar of copper or antimony, say -copper, soldered to a bar of bismuth, as in Fig. 12. Let us now heat -one of the junctions, while the other remains cool. It will be found -that a current of positive electricity circulates round the bar, in -the direction of the arrow-head, going from the bismuth to the copper -across the heated junction, the existence of which may be detected by -means of a compass needle, as we see in the figure. - -[Illustration: Fig. 12.] - -Here, then, we have a case in which heat energy goes out of existence, -and is converted into that of an electric current, and we may even -arrange matters so as to make, on this principle, an instrument which -shall be an extremely delicate test of the existence of heat. - -By having a number of junctions of bismuth and antimony, as in Fig. -13, and heating the upper set, while the lower remain cool, we get a -strong current going from the bismuth to the antimony across the heated -junctions, and we may pass the current so produced round the wire of -a galvanometer, and thus, by increasing the number of our junctions, -and also by using a very delicate galvanometer, we may get a very -perceptible effect for the smallest heating of the upper junctions. -This arrangement is called the _thermopile_, and, in conjunction with -the reflecting galvanometer, it affords the most delicate means known -for detecting small quantities of heat. - -[Illustration: Fig. 13.] - -162. The last transmutation on our list with respect to absorbed heat -is that in which this species of energy is transformed into _radiant -light and heat_. This takes place whenever a hot body cools in an open -space--the sun, for instance, parts with a large quantity of his heat -in this way; and it is due, in part at least, to this process that -a hot body cools in air, and wholly to it that such a body cools in -vacuo. It is, moreover, due to the penetration of our eye by radiant -energy that we are able to see hot bodies, and thus the very fact that -we see them implies that they are parting with their heat. - -Radiant energy moves through space with the enormous velocity of -188,000 miles in one second. It takes about eight minutes to come -from the sun to our earth, so that if our luminary were to be suddenly -extinguished, we should have eight minutes respite before the -catastrophe overtook us. Besides the rays that affect the eye, there -are others which we cannot see, and which may therefore be termed dark -rays. A body, for instance, may not be hot enough to be self-luminous, -and yet it may be rapidly cooling and changing its heat into radiant -energy, which is given off by the body, even although neither the eye -nor the touch may be competent to detect it. It may nevertheless be -detected by the thermopile, which was described in Art. 161. We thus -see how strong is the likeness between a heated body and a sounding -one. For just as a sounding body gives out part of its sound energy -to the atmosphere around it, so does a heated body give out part of -its heat energy to the ethereal medium around it. When, however, we -consider the rates of motion of these energies through their respective -media, there is a mighty difference between the two, sound travelling -through the air with the velocity of 1100 feet a second, while radiant -energy moves over no less a space than 188,000 miles in the same -portion of time. - - -_Chemical Separation._ - -163. We now come to the energy denoted by chemical separation, such -as we possess when we have coal or carbon in one place, and oxygen in -another. Very evidently this form of energy of position is transmuted -into _heat_ when we burn the coal, or cause it to combine with the -oxygen of the air; and generally, whenever chemical combination -takes place, we have the production of heat, even although other -circumstances may interfere to prevent its recognition. - -Now, in accordance with the principle of conservation, it may be -expected that, if a definite quantity of carbon or of hydrogen be -burned under given circumstances, there will be a definite production -of heat; that is to say, a ton of coals or of coke, when burned, will -give us so many heat units, and neither more or less. We may, no doubt, -burn our ton in such a way as to economize more or less of the heat -produced; but, as far as the mere production of heat is concerned, if -the quantity and quality of the material burned and the circumstances -of combustion be the same, we expect the same amount of heat. - -164. The following table, derived from the researches of Andrews, and -those of Favre and Silbermann, shows us how many units of heat we may -get by burning a kilogramme of various substances. - - -UNITS _of_ HEAT _developed by_ COMBUSTION _in_ OXYGEN. - - Kilogrammes of Water raised 1° C. - Substance by the combustion of one kilogramme - Burned. of each substance. - - Hydrogen 34,135 - Carbon 7,990 - Sulphur 2,263 - Phosphorus 5,747 - Zinc 1,301 - Iron 1,576 - Tin 1,233 - Olefiant Gas 11,900 - Alcohol 7,016 - -165. There are other methods, besides combustion, by which chemical -combination takes place. - -When, for instance, we plunge a piece of metallic iron into a solution -of copper, we find that when we take it out, its surface is covered -with copper. Part of the iron has been dissolved, taking the place of -the copper, which has therefore been thrown, in its metallic state, -upon the surface of the iron. Now, in this operation heat is given -out--we have in fact burned, or oxidized, the iron, and we are thus -furnished with a means of arranging the metals, beginning with that -which gives out most heat, when used to displace the metal at the other -extremity of the series. - -166. The following list has been formed, on this principle, by Dr. -Andrews:-- - - 1. Zinc - 2. Iron - 3. Lead - 4. Copper - 5. Mercury - 6. Silver - 7. Platinum - ---that is to say, the metal platinum can be displaced by any other -metal of the series, but we shall get most heat if we use zinc to -displace it. - -We may therefore assume that if we displace a definite quantity of -platinum by a definite quantity of zinc, we shall get a definite amount -of heat. Suppose, however, that instead of performing the operation -in one step, we make two of it. Let us, for instance, first of all -displace copper by means of zinc, and then platinum by means of copper. -Is it not possible that the one of these processes may be more fruitful -in heat giving than the other? Now, Andrews has shown us that we cannot -gain an advantage over Nature in this way, and that if we use our zinc -first of all to displace iron, or copper, or lead, and then use this -metal to displace platinum, we shall obtain just the very same amount -of heat as if we had used the zinc to displace the platinum at once. - -167. It ought here to be mentioned that, very generally, chemical -action is accompanied with a change of molecular condition. - -A solid, for instance, may be changed into a liquid, or a gas into -a liquid. Sometimes the one change counteracts the other as far as -apparent heat is concerned; but sometimes, too, they co-operate -together to increase the result. Thus, when a gas is absorbed by water, -much heat is evolved, and we may suppose the result to be due in part -to chemical combination, and in part to the condensation of the gas -into a liquid, by which means its latent heat is rendered sensible. On -the other hand, when a liquid unites with a solid, or when two solids -unite with one another, and the product is a liquid, we have very often -the absorption of heat, the heat rendered latent by the dissolution -of the solid being more than that generated by combination. Freezing -mixtures owe their cooling properties to this cause; thus, if snow and -salt be mixed together, they liquefy each other, and the result is -brine of a temperature much lower than that of either the ingredients. - -168. When heterogeneous metals, such as zinc and copper, are soldered -together, we have apparently a conversion of the energy of chemical -separation into that of _electrical separation_. This was first -suggested by Volta as the origin of the electrical separation which -we see in the voltaic current, and recently its existence has been -distinctly proved by Sir W. Thomson. - -To render manifest this conversion of energy, let us solder a piece of -zinc and copper together--if we now test the bar by means of a delicate -electrometer we shall find that the zinc is positively, while the -copper is negatively, electrified. We have here, therefore, an instance -of the transmutation of one form of energy of position into another; so -much energy of chemical separation disappearing in order to produce so -much electrical separation. This explains the fact recorded in Art. 93, -where we saw that if a battery be insulated and its poles kept apart, -the one will be charged with positive, and the other with negative, -electricity. - -169. But further, when such a voltaic battery is in action, we have a -transmutation of chemical separation into _electricity in motion_. To -see this, let us consider what takes place in such a battery. - -Here no doubt the sources of electrical excitement are the points of -contact of the zinc and platinum, where, as we see by our last article, -we have electrical separation produced. But this of itself would not -produce a current, for an electrical current implies very considerable -energy, and must be fed by something. Now, in the voltaic battery we -have two things which accompany each other, and which are manifestly -connected together. In the first place we have the combustion, or -at least the oxidation and dissolution, of the zinc; and we have, -secondly, the production of a powerful current. Now, evidently, the -first of these is that which feeds the second, or, in other words, the -energy of chemical separation of the metallic zinc is transmuted into -that of an electrical current, the zinc being virtually burned in the -process of transmutation. - -170. Finally, as far as we are aware, the energy of chemical separation -is not directly transmuted into radiant light and heat. - - -_Electrical Separation._ - -171. In the first place the energy of electrical separation is -obviously transmuted into that of _visible motion_, when two oppositely -electrified bodies approach each other. - -172. Again, it is transmuted into a _current of electricity_, and -ultimately into heat, when a spark passes between two oppositely -electrified bodies. - -It ought, therefore, to be borne in mind that when the flash is seen -there is no longer electricity, what we see being merely air, or some -other material, intensely heated by the discharge. Thus a man might -be rendered insensible by a flash of lightning without his seeing the -flash--for the effect of the discharge upon the man, and its effect in -heating the air, might be phenomena so nearly simultaneous that the man -might become insensible before he could perceive the flash. - - -_Electricity in Motion._ - -173. This energy is transmuted into that of _visible motion_ when two -wires conveying electrical currents in the same direction attract each -other. When, for instance, two circular currents float on water, both -going in the direction of the hands of a watch, we have seen from Art. -100 that they will move towards each other. Now, here there is, in -truth, a lessening of the intensity of each current when the motion is -taking place, for we know (Art. 104) that when a circuit is moved into -the presence of another circuit conveying a current, there is produced -by induction a current in the opposite direction; and hence we perceive -that, when two similar currents approach each other, each is diminished -by means of this inductive influence--in fact, a certain amount of -current energy disappears from existence in order that an equivalent -amount of the energy of visible motion may be produced. - -174. Electricity in motion is transmuted into _heat_ during the passage -of a current along a thin wire, or any badly conducting substance--the -wire is heated in consequence, and may even become white hot. Most -frequently the energy of an electric current is spent in heating the -wires and other materials that form the circuit. Now, the energy -of such a current is fed by the burning or oxidation of the metal -(generally zinc) which is used in the circuit, so that the ultimate -effect of this combustion is the heating of the various wires and other -materials through which the current passes. - -175. We may, in truth, burn or oxidize zinc in two ways--we may oxidize -it, as we have just seen, in the voltaic battery, and we shall find -that by the combustion of a kilogramme of zinc a definite amount of -heat is produced. Or we may oxidize our zinc by dissolving it in acid -in a single vessel, when, without going through the intermediate -process of a current, we shall get just as much heat out of a -kilogramme of zinc as we did in the former case. In fact, whether we -oxidize our zinc by the battery, or in the ordinary way, the quantity -of heat produced will always bear the same relation to the quantity of -zinc consumed; the only difference being that, in the ordinary way of -oxidizing zinc, the heat is generated in the vessel containing the zinc -and acid, while in the battery it may make its appearance a thousand -miles away, if we have a sufficiently long wire to convey our current. - -176. This is, perhaps, the right place for alluding to a discovery -of Peltier, that a current of positive electricity passing across a -junction of bismuth and antimony in the direction from the bismuth to -the antimony appears to produce cold. - -[Illustration: Fig. 14.] - -To understand the significance of this fact we must consider it in -connection with the thermo-electric current, which we have seen, from -Art. 161, is established in a circuit of bismuth and antimony, of -which one junction is hotter than the other. Suppose we have a circuit -of this kind with both its junctions at the temperature of 100° C. -to begin with. Suppose, next, that while we protect one junction, we -expose the other to the open air--it will, of course, lose heat, so -that the protected junction will now be hotter than the other. The -consequence will be (Art. 161) that a current of positive electricity -will pass along the protected junction from the bismuth to the -antimony. - -Now, here we have an apparent anomaly, for the circuit is cooling--that -is to say, it is losing energy--but at the very same time it is -manifesting energy in another shape, namely, in that of an electric -current, which is circulating round it. Clearly, then, some of the heat -of this circuit must be spent in generating this current; in fact, -we should expect the circuit to act as a heat engine, only producing -current energy instead of mechanical energy, and hence (Art. 152) -we should expect to see a conveyance of heat from the hotter to the -colder parts of the circuit. Now, this is precisely what the current -does, for, passing along the hotter junction, in the direction of the -arrow-head, it cools that junction, and heats the colder one at C,--in -other words, it carries heat from the hotter to the colder parts of the -circuit. We should have been very much surprised had such a current -cooled C and heated H, for then we should have had a manifestation of -current energy, accompanied with the conveyance of heat from a colder -to a hotter substance, which is against the principle of Art. 152. - -177. Finally, the energy of electricity in motion is converted into -that of _chemical separation_, when a current of electricity is made to -decompose a body. Part of the energy of the current is spent in this -process, and we shall get so much less heat from it in consequence. -Suppose, for instance, that by oxidizing so much zinc in the battery we -get, under ordinary circumstances, 100 units of heat. Let us, however, -set the battery to decompose water, and we shall probably find that by -oxidizing the same amount of zinc we get now only 80 units of heat. -Clearly, then, the deficiency or 20 units have gone to decompose the -water. Now, if we explode the mixed gases which are the result of the -decomposition, we shall get back these 20 units of heat precisely, and -neither more nor less; and thus we see that amid all such changes the -quantity of energy remains the same. - - -_Radiant Energy._ - -178. This form of energy is converted into _absorbed heat_ whenever -it falls upon an opaque substance--some of it, however, is generally -conveyed away by reflexion, but the remainder is absorbed by the body, -and consequently heats it. - -It is a curious question to ask what becomes of the radiant light from -the sun that is not absorbed either by the planets of our system, or by -any of the stars. We can only reply to such a question, that _as far as -we can judge from our present knowledge_, the radiant energy that is -not absorbed must be conceived to be traversing space at the rate of -188,000 miles a second. - -179. There is only one more transmutation of radiant energy that we -know of, and that is when it promotes _chemical separation_. Thus, -certain rays of the sun are known to have the power of decomposing -chloride of silver, and other chemical compounds. Now, in all such -cases there is a transmutation of radiant energy into that of chemical -separation. The sun’s rays, too, decompose carbonic acid in the leaves -of plants, the carbon going to form the woody fibre of the plant, while -the oxygen is set free into the air; and of course a certain proportion -of the energy of the solar rays is consumed in promoting this change, -and we have so much less heating effect in consequence. - -But all the solar rays have not this power--for the property of -promoting chemical change is confined to the blue and violet rays, -and some others which are not visible to the eye. Now, these rays are -entirely absent from the radiation of bodies at a comparatively low -temperature, such as an ordinary red heat, so that a photographer would -find it impossible to obtain the picture of a red-hot body, whose only -light was in itself. - -180. The actinic, or chemically active, rays of the sun decompose -carbonic acid in the leaves of plants, and they disappear in -consequence, or are absorbed; this may, therefore, be the reason why -very few such rays are either reflected or transmitted from a sun-lit -leaf, in consequence of which the photographer finds it difficult to -obtain an image of such a leaf; in other words, the rays which would -have produced a chemical change on his photographic plate have all been -used up by the leaf for peculiar purposes of its own. - -181. And here it is important to bear in mind that while animals in -the act of breathing consume the oxygen of the air, turning it into -carbonic acid, plants, on the other hand, restore the oxygen to the -air; thus the two kingdoms, the animal and the vegetable, work into -each other’s hands, and the purity of the atmosphere is kept up. - - -FOOTNOTES: - -[4] This explanation was first given by Professors Thomson and Tait -in their Natural Philosophy, and by Dr. Frankland in a lecture at the -Royal Institution of London. - -[5] _See_ De La Rue, Stewart, and Loewy’s researches on Solar Physics. - -[6] _See_ the Magnetic Researches of Sir E. Sabine, also C. Meldrum on -the Periodicity of Cyclones. - - - - -CHAPTER V. - -_HISTORICAL SKETCH: THE DISSIPATION OF ENERGY._ - - -182. In the last chapter we have endeavoured to exhibit the various -transmutations of energy, and, while doing so, to bring forward -evidence in favour of the theory of conservation, showing that it -enables us to couple together known laws, and also to discover new -ones--showing, in fine, that it bears about with it all the marks of a -true hypothesis. - -It may now, perhaps, be instructive, to look back and endeavour to -trace the progress of this great conception, from its first beginning -among the ancients, up to its triumphant establishment by the labours -of Joule and his fellow-workers. - -183. Mathematicians inform us that if matter consists of atoms or -small parts, which are actuated by forces depending only upon the -distances between these parts, and not upon the velocity, then it may -be demonstrated that the law of conservation of energy will hold good. -Thus we see that conceptions regarding atoms and their forces are -allied to conceptions regarding energy. A medium of some sort pervading -space seems also necessary to our theory. In fine, a universe composed -of atoms, with some sort of medium between them, is to be regarded as -the machine, and the laws of energy as the laws of working of this -machine. It may be that a theory of atoms of this sort, with a medium -between them, is not after all the simplest, but we are probably not -yet prepared for any more general hypothesis. Now, we have only to -look to our own solar system, in order to see on a large scale an -illustration of this conception, for there we have the various heavenly -bodies attracting one another, with forces depending only on the -distances between them, and independent of the velocities; and we have -likewise a medium of some sort, in virtue of which radiant energy is -conveyed from the sun to the earth. Perhaps we shall not greatly err -if we regard a molecule as representing on a small scale something -analogous to the solar system, while the various atoms which constitute -the molecule may be likened to the various bodies of the solar system. -The short historical sketch which we are about to give will embrace, -therefore, along with energy, the progress of thought and speculation -with respect to atoms and also with respect to a medium, inasmuch as -these subjects are intimately connected with the doctrines of energy. - - -_Heraclitus on Energy._ - -184. Heraclitus, who flourished at Ephesus, B.C. 500, declared that -fire was the great cause, and that all things were in a perpetual -flux. Such an expression will no doubt be regarded as very vague in -these days of precise physical statements; and yet it seems clear that -Heraclitus must have had a vivid conception of the innate restlessness -and energy of the universe, a conception allied in character to, and -only less precise than that of modern philosophers, who regard matter -as essentially dynamical. - - -_Democritus on Atoms._ - -185. Democritus, who was born 470 B.C., was the originator of the -doctrine of atoms, a doctrine which in the hands of John Dalton -has enabled the human mind to lay hold of the laws which regulate -chemical changes, as well as to picture to itself what is there taking -place. Perhaps there is no doctrine that has nowadays a more intimate -connection with the industries of life than this of atoms, and it -is probable that no intelligent director of chemical industry among -civilized nations fails to picture to his own mind, by means of this -doctrine, the inner nature of the changes which he sees with his eyes. -Now, it is a curious circumstance that Bacon should have lighted upon -this very doctrine of atoms, in order to point one of his philosophical -morals. - - “Nor is it less an evil” (says he), “that in their philosophies and - contemplations men spend their labour in investigating and treating of - the first principles of things, and the extreme limits of nature, when - all that is useful and of avail in operation is to be found in what is - intermediate. Hence it happens that men continue to abstract Nature - till they arrive at potential and unformed matter; and again they - continue to divide Nature, until they have arrived at the atom; things - which, even if true, can be of little use in helping on the fortunes - of men.” - -Surely we ought to learn a lesson from these remarks of the great -Father of experimental science, and be very cautious before we dismiss -any branch of knowledge or train of thought as essentially unprofitable. - - -_Aristotle on a Medium._ - -186. As regards the existence of a medium, it is remarked by Whewell -that the ancients also caught a glimpse of the idea of a medium, by -which the qualities of bodies, as colours and sounds are perceived, and -he quotes the following from Aristotle:-- - - “In a void there could be no difference of up and down; for, as in - nothing there are no differences, so there are none in a privation or - negation.” - -Upon this the historian of science remarks, “It is easily seen that -such a mode of reasoning elevates the familiar forms of language, and -the intellectual connexions of terms, to a supremacy over facts.” - -Nevertheless, may it not be replied that our conceptions of matter are -deduced from the familiar experience, that certain portions of space -affect us in a certain manner; and, consequently, are we not entitled -to say there must be something where we experience the difference of -up or down? Is there, after all, a very great difference between this -argument and that of modern physicists in favour of a plenum, who tell -us that matter cannot act where it is not? - -Aristotle seems also to have entertained the idea that light is not any -body, or the emanation of any body (for that, he says, would be a kind -of body), and that therefore light is an energy or act. - - -_The Ideas of the Ancients were not Prolific._ - -187. These quotations render it evident that the ancients had, in some -way, grasped the idea of the essential unrest and energy of things. -They had also the idea of small particles or atoms, and, finally, of a -medium of some sort. And yet these ideas were not prolific--they gave -rise to nothing new. - -Now, while the historian of science is unquestionably right in his -criticism of the ancients, that their ideas were not distinct and -appropriate to the facts, yet we have seen that they were not wholly -ignorant of the most profound and deeply-seated principles of the -material universe. In the great hymn chanted by Nature, the fundamental -notes were early heard, but yet it required long centuries of patient -waiting for the practised ear of the skilled musician to appreciate -the mighty harmony aright. Or, perhaps, the attempts of the ancients -were as the sketches of a child who just contrives to exhibit, in a -rude way, the leading outlines of a building; while the conceptions -of the practised physicist are more allied to those of the architect, -or, at least, of one who has realized, to some extent, the architect’s -views. - -188. The ancients possessed great genius and intellectual power, but -they were deficient in physical conceptions, and, in consequence, -their ideas were not prolific. It cannot indeed be said that we of the -present age are deficient in such conceptions; nevertheless, it may be -questioned whether there is not a tendency to rush into the opposite -extreme, and to work physical conceptions to an excess. Let us be -cautious that in avoiding Scylla, we do not rush into Charybdis. For -the universe has more than one point of view, and there are possibly -regions which will not yield their treasures to the most determined -physicists, armed only with kilogrammes and metres and standard clocks. - - -_Descartes, Newton, and Huyghens on a Medium._ - -189. In modern times Descartes, author of the vertical hypothesis, -necessarily presupposed the existence of a medium in inter-planetary -spaces, but on the other hand he was one of the originators of that -idea which regards light as a series of particles shot out from a -luminous body. Newton likewise conceived the existence of a medium, -although he became an advocate of the theory of emission. It is -to Huyghens that the credit belongs of having first conceived the -undulatory theory of light with sufficient distinctness to account for -double refraction. After him, Young, Fresnel, and their followers, -have greatly developed the theory, enabling it to account for the most -complicated and wonderful phenomena. - - -_Bacon on Heat._ - -190. With regard to the nature of heat, Bacon, whatever may be thought -of his arguments, seems clearly to have recognized it as a species -of motion. He says, “From these instances, viewed together and -individually, the nature of which heat is the limitation seems to be -motion;” and again he says, “But when we say of motion that it stands -in the place of a genus to heat, we mean to convey, not that _heat_ -generates _motion_ or _motion heat_ (although even both may be true in -some cases), but that essential heat is motion and nothing else.” - -Nevertheless it required nearly three centuries before the true theory -of heat was sufficiently rooted to develop into a productive hypothesis. - - -_Principle of Virtual Velocities._ - -191. In a previous chapter we have already detailed the labours in -respect of heat of Davy, Rumford, and Joule. Galileo and Newton, if -they, did not grasp the dynamical nature of heat, had yet a clear -conception of the functions of a machine. The former saw that what we -gain in power we lose in space; while the latter went further, and saw -that a machine, if left to itself, is strictly limited in the amount of -work which it can accomplish, although its energy may vary from that of -motion to that of position, and back again, according to the geometric -laws of the machine. - - -_Rise of true Conceptions regarding Work._ - -192. There can, we think, be no question that the great development -of industrial operations in the present age has indirectly furthered -our conceptions regarding work. Humanity invariably strives to escape -as much as possible from hard work. In the days of old those who had -the power got slaves to work for them; but even then the master had -to give some kind of equivalent for the work done. For at the very -lowest a slave is a machine, and must be fed, and is moreover apt to -prove a very troublesome machine if not properly dealt with. The great -improvements in the steam engine, introduced by Watt, have done as -much, perhaps, as the abolition of slavery to benefit the working man. -The hard work of the world has been put upon iron shoulders, that do -not smart; and, in consequence, we have had an immense extension of -industry, and a great amelioration in the position of the lower classes -of mankind. But if we have transferred our hard work to machines, it is -necessary to know how to question a machine--how to say to it, At what -rate can you labour? how much work can you turn out in a day? It is -necessary, in fact, to have the clearest possible idea of what work is. - -Our readers will see from all this that men are not likely to err in -their method of measuring work. The principles of measurement have -been stamped as it were with a brand into the very heart and brain of -humanity. To the employer of machinery or of human labour, a false -method of measuring work simply means ruin; he is likely, therefore, -to take the greatest possible pains to arrive at accuracy in his -determination. - - -_Perpetual Motion._ - -193. Now, amid the crowd of workers smarting from the curse of labour, -there rises up every now and then an enthusiast, who seeks to escape -by means of an artifice from this insupportable tyranny of work. -Why not construct a machine that will go on giving you work without -limit without the necessity of being fed in any way. Nature must -have some weak point in her armour; there must surely be some way -of getting round her; she is only tyrannous on the surface, and in -order to stimulate our ingenuity, but will yield with pleasure to the -persistence of genius. - -Now, what can the man of science say to such an enthusiast? He cannot -tell him that he is intimately acquainted with all the forces of -Nature, and can prove that perpetual motion is impossible; for, in -truth, he knows very little of these forces. But he does think that -he has entered into the spirit and design of Nature, and therefore he -denies at once the possibility of such a machine. But he denies it -intelligently, and works out this denial of his into a theory which -enables him to discover numerous and valuable relations between the -properties of matter--produces, in fact, the laws of energy and the -great principle of conservation. - - -_Theory of Conservation._ - -194. We have thus endeavoured to give a short sketch of the history of -energy, including its allied problems, up to the dawn of the strictly -scientific period. We have seen that the unfruitfulness of the earlier -views was due to a want of scientific clearness in the conceptions -entertained, and we have now to say a few words regarding the theory of -conservation. - -Here also the way was pointed out by two philosophers, namely, Grove -in this country, and Mayer on the continent, who showed certain -relations between the various forms of energy; the name of Séguin -ought likewise to be mentioned. Nevertheless, to Joule belongs the -honour of establishing the theory on an incontrovertible basis: for, -indeed, this is preeminently a case where speculation has to be tested -by unimpeachable experimental evidence. Here the magnitude of the -principle is so vast, and its importance is so great, that it requires -the strong fire of genius, joined to the patient labours of the -scientific experimentalist, to forge the rough ore into a good weapon -that will cleave its way through all obstacles into the very citadel of -Nature, and into her most secret recesses. - -Following closely upon the labours of Joule, we have those of William -and James Thomson, Helmholtz, Rankine, Clausius, Tait, Andrews, -Maxwell, who, along with many others, have advanced the subject; and -while Joule gave his chief attention to the laws which regulate the -transmutation of mechanical energy into heat, Thomson, Rankine, and -Clausius gave theirs to the converse problem, or that which relates to -the transmutation of heat into mechanical energy. Thomson, especially, -has pushed forward so resolutely from this point of view that he has -succeeded in grasping a principle scarcely inferior in importance to -that of the conservation of energy itself, and of this principle it -behoves us now to speak. - - -_Dissipation of Energy._ - -195. Joule, we have said, proved the law according to which work may -be changed into heat; and Thomson and others, that according to which -heat may be changed into work. Now, it occurred to Thomson that there -was a very important and significant difference between these two laws, -consisting in the fact that, while you can with the greatest ease -transform work into heat, you can by no method in your power transform -all the heat back again into work. In fact, the process is not a -reversible one; and the consequence is that the mechanical energy of -the universe is becoming every day more and more changed into heat. - -It is easily seen that if the process were reversible, one form of a -perpetual motion would not be impossible. For, without attempting to -create energy by a machine, all that would be needed for a perpetual -motion would be the means of utilizing the vast stores of heat that -lie in all the substances around us, and converting them into work. -The work would no doubt, by means of friction and otherwise, be -ultimately reconverted into heat; but if the process be reversible, the -heat could again be converted into work, and so on for ever. But the -irreversibility of the process puts a stop to all this. In fact, I may -convince myself by rubbing a metal button on a piece of wood how easily -work can be converted into heat, while the mind completely fails to -suggest any method by which this heat can be reconverted into work. - -Now, if this process goes on, and always in one direction, there can be -no doubt about the issue. The mechanical energy of the universe will -be more and more transformed into universally diffused heat, until the -universe will no longer be a fit abode for living beings. - -The conclusion is a startling one, and, in order to bring it more -vividly before our readers, let us now proceed to acquaint ourselves -with the various forms of useful energy that are at present at our -disposal, and at the same time endeavour to trace the ultimate sources -of these supplies. - - -_Natural Energies and their Sources._ - -196. Of energy in repose we have the following varieties:--(1.) The -energy of fuel. (2.) That of food. (3.) That of a head of water. (4.) -That which may be derived from the tides. (5.) The energy of chemical -separation implied in native sulphur, native iron, &c. - -Then, with regard to energy in action, we have mainly the following -varieties:-- - -(1.) The energy of air in motion. (2.) That of water in motion. - - -_Fuel._ - -197. Let us begin first with the energy implied in fuel. We can, of -course, burn fuel, or cause it to combine with the oxygen of the air; -and we are thereby provided with large quantities of heat of high -temperature, by means of which we may not only warm ourselves and cook -our food, but also drive our heat-engines, using it, in fact, as a -source of mechanical power. - -Fuel is of two varieties--wood and coal. Now, if we consider the origin -of these we shall see that they are produced by the sun’s rays. Certain -of these rays, as we have already remarked (Art. 180), decompose -carbonic acid in the leaves of plants, setting free the oxygen, while -the carbon is used for the structure or wood of the plant. Now, the -energy of these rays is spent in this process, and, indeed, there -is not enough of such energy left to produce a good photographic -impression of the leaf of a plant, because it is all spent in making -wood. - -We thus see that the energy implied in wood is derived from the sun’s -rays, and the same remark applies to coal. Indeed, the only difference -between wood and coal is one of age: wood being recently turned out -from Nature’s laboratory, while thousands of years have elapsed since -coal formed the leaves of living plants. - -198. We are, therefore, perfectly justified in saying that the energy -of fuel is derived from the sun’s rays;[7] coal being the store which -Nature has laid up as a species of capital for us, while wood is our -precarious yearly income. - -We are thus at present very much in the position of a young heir, who -has only recently come into his estate, and who, not content with the -income, is rapidly squandering his realized property. This subject has -been forcibly brought before us by Professor Jevons, who has remarked -that not only are we spending our capital, but we are spending the most -available and valuable part of it. For we are now using the surface -coal; but a time will come when this will be exhausted, and we shall be -compelled to go deep down for our supplies. Now, regarded as a source -of energy, such supplies, if far down, will be less effective, for we -have to deduct the amount of energy requisite in order to bring them to -the surface. The result is that we must contemplate a time, however far -distant, when our supplies of coal will be exhausted, and we shall be -compelled to resort to other sources of energy. - - -_Food._ - -199. The energy of food is analogous to that of fuel, and serves -similar purposes. For just as fuel may be used either for producing -heat or for doing work, so food has a twofold office to perform. In -the first place, by its gradual oxidation, it keeps up the temperature -of the body; and in the next place it is used as a source of energy, -on which to draw for the performance of work. Thus a man or a horse -that works a great deal requires to eat more food than if he does not -work at all. Thus, also, a prisoner condemned to hard labour requires -a better diet than one who does not work, and a soldier during the -fatigues of war finds it necessary to eat more than during a time of -peace. - -Our food may be either of animal or vegetable origin--if it be the -latter, it is immediately derived, like fuel, from the energy of the -sun’s rays; but if it be the former, the only difference is that it has -passed through the body of an animal before coming to us: the animal -has eaten grass, and we have eaten the animal. - -In fact, we make use of the animal not only as a variety of nutritious -food, but also to enable us indirectly to utilize those vegetable -products, such as grasses, which we could not make use of directly with -our present digestive organs. - - -_Head of Water._ - -200. The energy of a head of water, like that of fuel and food, is -brought about by the sun’s rays. For the sun vaporizes the water, -which, condensed again in upland districts, becomes available as a head -of water. - -There is, however, the difference that fuel and food are due to the -actinic power of the sun’s rays, while the evaporation and condensation -of water are caused rather by their heating effect. - - -_Tidal Energy._ - -201. The energy derived from the tides has, however, a different -origin. In Art. 133 we have endeavoured to show how the moon acts upon -the fluid portions of our globe, the result of this action being a very -gradual stoppage of the energy of rotation of the earth. - -It is, therefore, to this motion of rotation that we must look as the -origin of any available energy derived from tidal mills. - - -_Native Sulphur, &c._ - -202. The last variety of available energy of position in our list is -that implied in native sulphur, native iron, &c. It has been remarked -by Professor Tait, to whom this method of reviewing our forces is due, -that this may be the primeval form of energy, and that the interior of -the earth may, as far as we know, be wholly composed of matter in its -uncombined form. As a source of available energy it is, however, of no -practical importance. - - -_Air and Water in Motion._ - -203. We proceed next to those varieties of available energy which -represent motion, the chief of which are air in motion and water in -motion. It is owing to the former that the mariner spreads his sail, -and carries his vessel from one part of the earth’s surface to another, -and it is likewise owing to the same influence that the windmill grinds -our corn. Again, water in motion is used perhaps even more frequently -than air in motion as a source of motive power. - -Both these varieties of energy are due without doubt to the heating -effect of the sun’s rays. We may, therefore, affirm that with the -exception of the totally insignificant supply of native sulphur, &c., -and the small number of tidal mills which may be in operation, all our -available energy is due to the sun. - - -_The Sun--a Source of High Temperature Heat._ - -204. Let us, therefore, now for a moment direct our attention to that -most wonderful source of energy, the Sun. - -We have here a vast reservoir of high temperature heat; now, this -is a kind of superior energy which has always been in much request. -Numberless attempts have been made to construct a perpetual light, -just as similar attempts have been made to construct a perpetual -motion, with this difference, that a perpetual light was supposed to -result from magical powers, while a perpetual motion was attributed to -mechanical skill. - -Sir Walter Scott alludes to this belief in his description of the grave -of Michael Scott, which is made to contain a perpetual light. Thus the -Monk who buried the wizard tells William of Deloraine-- - - “Lo, Warrior! now the Cross of Red - Points to the Grave of the mighty dead; - Within it burns a wondrous light, - To chase the spirits that love the night. - That lamp shall burn unquenchably - Until the eternal doom shall be.” - -And again, when the tomb was opened, we read-- - - “I would you had been there to see - How the light broke forth so gloriously, - Stream’d upward to the chancel roof, - And through the galleries far aloof! - No earthly flame blazed e’er so bright.” - -No earthly flame--there the poet was right--certainly not of this -earth, where light and all other forms of superior energy are -essentially evanescent. - - -_A Perpetual Light Impossible._ - -205. In truth, our readers will at once perceive that a perpetual light -is only another name for a perpetual motion, because we can always -derive visible energy out of high temperature heat--indeed, we do so -every day in our steam engines. - -When, therefore, we burn coal, and cause it to combine with the -oxygen of the air, we derive from the process a large amount of high -temperature heat. But is it not possible, our readers may ask, to -take the carbonic acid which results from the combustion, and by -means of low temperature heat, of which we have always abundance -at our disposal, change it back again into carbon and oxygen? All -this would be possible if what may be termed the temperature of -disassociation--that is to say, the temperature at which carbonic acid -separates into its constituents--were a low temperature, and it would -also be possible if rays from a source of low temperature possessed -sufficient actinic power to decompose carbonic acid. - -But neither of these is the case. Nature will not be caught in a -trap of this kind. As if for the very purpose of stopping all such -speculations, the temperatures of disassociation for such substances as -carbonic acid are very high, and the actinic rays capable of causing -their decomposition belong only to sources of exceedingly high -temperature, such as the sun.[8] - - -_Is the Sun an Exception?_ - -206. We may, therefore, take it for granted that a perpetual light, -like a perpetual motion, is an impossibility; and we have then to -inquire if the same argument applies to our sun, or if an exception -is to be made in his favour. Does the sun stand upon a footing of his -own, or is it merely a question of time with him, as with all other -instances of high temperature heat? Before attempting to answer this -question let us inquire into the probable origin of the sun’s heat. - - -_Origin of the Sun’s Heat._ - -207. Now, some might be disposed to cut the Gordian knot of such an -inquiry by asserting that our luminary was at first created hot; yet -the scientific mind finds itself disinclined to repose upon such an -assertion. We pick up a round pebble from the beach, and at once -acknowledge there has been some physical cause for the shape into which -it has been worn. And so with regard to the heat of the sun, we must -ask ourselves if there be not some cause not wholly imaginary, but one -which we know, or at least suspect, to be perhaps still in operation, -which can account for the heat of the sun. - -Now, here it is more easy to show what cannot account for the sun’s -heat than what can do so. We may, for instance, be perfectly certain -that it cannot have been caused by chemical action. The most probable -theory is that which was first worked out by Helmholtz and Thomson;[9] -and which attributes the heat of the sun to the primeval energy of -position possessed by its particles. In other words, it is supposed -that these particles originally existed at a great distance from each -other, and that, being endowed with the force of gravitation, they have -since gradually come together, while in this process heat has been -generated just as it would be if a stone were dropped from the top of a -cliff towards the earth. - -208. Nor is this case wholly imaginary, but we have some reason -for thinking that it may still be in operation in the case of -certain nebulæ which, both in their constitution as revealed by the -spectroscope, and in their general appearance, impress the beholder -with the idea that they are not yet fully condensed into their ultimate -shape and size. - -If we allow that by this means our luminary has obtained his wonderful -store of high-class energy, we have yet to inquire to what extent this -operation is going on at the present moment. Is it only a thing of the -past, or is it a thing also of the present? I think we may reply that -the sun cannot be condensing very fast, at least, within historical -times. For if the sun were sensibly larger than at present his total -eclipse by the moon would be impossible. Now, such eclipses have -taken place, at any rate, for several thousands of years. Doubtless a -small army of meteors may be falling into our luminary, which would -by this fall tend to augment his heat; yet the supply derived from -this source must surely be insignificant. But if the sun be not at -present condensing so fast as to derive any sufficient heat from this -process, and if his energy be very sparingly recruited from without, -it necessarily follows that he is in the position of a man whose -expenditure exceeds his income. He is living upon his capital, and is -destined to share the fate of all who act in a similar manner. We must, -therefore, contemplate a future period when he will be poorer in energy -than he is at present, and a period still further in the future when he -will altogether cease to shine. - - -_Probable Fate of the Universe._ - -209. If this be the fate of the high temperature energy of the -universe, let us think for a moment what will happen to its visible -energy. We have spoken already about a medium pervading space, the -office of which appears to be to degrade and ultimately extinguish -all differential motion, just as it tends to reduce and ultimately -equalize all difference of temperature. Thus the universe would -ultimately become an equally heated mass, utterly worthless as far as -the production of work is concerned, since such production depends upon -difference of temperature. - -Although, therefore, in a strictly mechanical sense, there is a -conservation of energy, yet, as regards usefulness or fitness -for living beings, the energy of the universe is in process of -deterioration. Universally diffused heat forms what we may call the -great waste-heap of the universe, and this is growing larger year by -year. At present it does not sensibly obtrude itself, but who knows -that the time may not arrive when we shall be practically conscious of -its growing bigness? - -210. It will be seen that in this chapter we have regarded the -universe, not as a collection of matter, but rather as an energetic -agent--in fact, as a lamp. Now, it has been well pointed out by -Thomson, that looked at in this light, the universe is a system that -had a beginning and must have an end; for a process of degradation -cannot be eternal. If we could view the universe as a candle not lit, -then it is perhaps conceivable to regard it as having been always in -existence; but if we regard it rather as a candle that has been lit, -we become absolutely certain that it cannot have been burning from -eternity, and that a time will come when it will cease to burn. We are -led to look to a beginning in which the particles of matter were in -a diffuse chaotic state, but endowed with the power of gravitation, -and we are led to look to an end in which the whole universe will be -one equally heated inert mass, and from which everything like life or -motion or beauty will have utterly gone away. - - -FOOTNOTES: - -[7] This fact seems to have been known at a comparatively early period -to Herschel and the elder Stephenson. - -[8] This remark is due to Sir William Thomson. - -[9] Mayer and Waterston seem first to have caught the rudiments of this -idea. - - - - -CHAPTER VI. - -_THE POSITION OF LIFE._ - - -211. We have hitherto confined ourselves almost entirely to a -discussion of the laws of energy, as these affect inanimate matter, -and have taken little or no account of the position of life. We have -been content very much to remain spectators of the contest, apparently -forgetful that we are at all concerned in the issue. But the conflict -is not one which admits of on-lookers,--it is a universal conflict in -which we must all take our share. It may not, therefore, be amiss if we -endeavour to ascertain, as well as we can, our true position. - - -_Twofold nature of Equilibrium._ - -212. One of our earliest mechanical lessons is on the twofold nature -of equilibrium. We are told that this may be of two kinds, _stable_ -and _unstable_, and a very good illustration of these two kinds is -furnished by an egg. Let us take a smooth level table, and place an egg -upon it; we all know in what manner the egg will lie on the table. -It will remain at rest, that is to say, it will be in equilibrium; -and not only so, but it will be in stable equilibrium. To prove -this, let us try to displace it with our finger, and we shall find -that when we remove the pressure the egg will speedily return to its -previous position, and will come to rest after one or two oscillations. -Furthermore, it has required a sensible expenditure of energy to -displace the egg. All this we express by saying that the egg is in -stable equilibrium. - - -_Mechanical Instability._ - -213. And now let us try to balance the egg upon its longer axis. -Probably, a sufficient amount of care will enable us to achieve this -also. But the operation is a difficult one, and requires great delicacy -of touch, and even after we have succeeded we do not know how long -our success may last. The slightest impulse from without, the merest -breath of air, may be sufficient to overturn the egg, which is now most -evidently in unstable equilibrium. If the egg be thus balanced at the -very edge of the table, it is quite probable that in a few minutes it -may topple over upon the floor; it is what we may call _an even chance_ -whether it will do so, or merely fall upon the table. Not that mere -chance has anything to do with it, or that its movements are without -a cause, but we mean that its movements are decided by some external -impulse so exceedingly small as to be utterly beyond our powers of -observation. In fact, before making the trial we have carefully -removed everything like a current of air, or want of level, or external -impulse of any kind, so that when the egg falls we are completely -unable to assign the origin of the impulse that has caused it to do so. - -214. Now, if the egg happens to fall over the table upon the floor, -there is a somewhat considerable transmutation of energy; for the -energy of position of the egg, due to the height which it occupied -on the table, has all at once been changed into energy of motion, in -the first place, and into heat in the second, when the egg comes into -contact with the floor. - -If, however, the egg happens to fall upon the table, the transmutation -of energy is comparatively small. - -It thus appears that it depends upon some external impulse, so -infinitesimally small as to elude our observation, whether the egg -shall fall upon the floor and give rise to a comparatively large -transmutation of energy, or whether it shall fall upon the table and -give rise to a transmutation comparatively small. - - -_Chemical Instability._ - -215. We thus see that a body, or system, in unstable equilibrium may -become subject to a very considerable transmutation of energy, arising -out of a very small cause, or antecedent. In the case now mentioned, -the force is that of gravitation, the arrangement being one of visible -mechanical instability. But we may have a substance, or system, in -which the force at work is not gravity, but chemical affinity, and the -substance, or system, may, under certain peculiar conditions, become -_chemically unstable_. - -When a substance is chemically unstable, it means that the slightest -impulse of any kind may determine a chemical change, just as in the -case of the egg the slightest impulse from without occasioned a -mechanical displacement. - -In fine, a substance, or system, chemically unstable bears a relation -to chemical affinity somewhat similar to that which a mechanically -unstable system bears to gravity. Gunpowder is a familiar instance -of a chemically unstable substance. Here the slightest spark may -prove the precursor of a sudden chemical change, accompanied by the -instantaneous and violent generation of a vast volume of heated gas. -The various explosive compounds, such as gun-cotton, nitro-glycerine, -the fulminates, and many more, are all instances of structures which -are chemically unstable. - - -_Machines are of two kinds._ - -216. When we speak of a structure, or a machine, or a system, we simply -mean a number of individual particles associated together in producing -some definite result. Thus, the solar system, a timepiece, a rifle, -are examples of inanimate machines; while an animal, a human being, -an army, are examples of animated structures or machines. Now, such -machines or structures are of two kinds, which differ from one another -not only in the object sought, but also in the means of attaining that -object. - -217. In the first place, we have structures or machines in which -systematic action is the object aimed at, and in which all the -arrangements are of a conservative nature, the element of instability -being avoided as much as possible. The solar system, a timepiece, -a steam-engine at work, are examples of such machines, and the -characteristic of all such is their _calculability_. Thus the skilled -astronomer can tell, with the utmost precision, in what place the -moon or the planet Venus will be found this time next year. Or again, -the excellence of a timepiece consists in its various hands pointing -accurately in a certain direction after a certain interval of time. In -like manner we may safely count upon a steamship making so many knots -an hour, at least while the outward conditions remain the same. In all -these cases we make our calculations, and we are not deceived--the end -sought is regularity of action, and the means employed is a stable -arrangement of the forces of nature. - -218. Now, the characteristics of the other class of machines are -precisely the reverse. - -Here the object aimed at is not a regular, but a sudden and violent -transmutation of energy, while the means employed are unstable -arrangements of natural forces. A rifle at full cock, with a -delicate hair-trigger, is a very good instance of such a machine, -where the slightest touch from without may bring about the explosion -of the gunpowder, and the propulsion of the ball with a very great -velocity. Now, such machines are eminently characterized by their -_incalculability_. - -219. To make our meaning clear, let us suppose that two sportsmen -go out hunting together, each with a good rifle and a good pocket -chronometer. After a hard day’s work, the one turns to his companion -and says:--“It is now six o’clock by my watch; we had better rest -ourselves,” upon which the other looks at his watch, and he would be -very much surprised and exceedingly indignant with the maker, if he did -not find it six o’clock also. Their chronometers are evidently in the -same state, and have been doing the same thing; but what about their -rifles? Given the condition of the one rifle, is it possible by any -refinement of calculation to deduce that of the other? We feel at once -that the bare supposition is ridiculous. - -220. It is thus apparent that, as regards energy, structures are -of two kinds. In one of these, the object sought is regularity of -action, and the means employed, a stable arrangement of natural -forces: while in the other, the end sought is freedom of action, and a -sudden transmutation of energy, the means employed being an unstable -arrangement of natural forces. - -The one set of machines are characterized by their calculability--the -other by their incalculability. The one set, when at work, are not -easily put wrong, while the other set are characterized by great -delicacy of construction. - - -_An Animal is a delicately-constructed Machine._ - -221. But perhaps the reader may object to our use of the rifle as an -illustration. - -For although it is undoubtedly a delicately-constructed machine, yet -a rifle does not represent the same surpassing delicacy as that, for -instance, which characterizes an egg balanced on its longer axis. Even -if at full cock, and with a hair trigger, we may be perfectly certain -it will not go off of its own accord. Although its object is to produce -a sudden and violent transmutation of energy, yet this requires to be -preceded by the application of an amount of energy, however small, to -the trigger, and if this be not spent upon the rifle, it will not go -off. There is, no doubt, delicacy of construction, but this has not -risen to the height of incalculability, and it is only when in the -hands of the sportsman that it becomes a machine upon the condition of -which we cannot calculate. - -Now, in making this remark, we define the position of the sportsman -himself in the Universe of Energy. - -The rifle is delicately constructed, but not surpassingly so; but -sportsman and rifle, together, form a machine of surpassing delicacy, -_ergo_ the sportsman himself is such a machine. We thus begin to -perceive that a human being, or indeed an animal of any kind, is -in truth a machine of a delicacy that is practically infinite, the -condition or motions of which we are utterly unable to predict. - -In truth, is there not a transparent absurdity in the very thought that -a man may become able to calculate his own movements, or even those of -his fellow? - - -_Life is like the Commander of an Army._ - -222. Let us now introduce another analogy--let us suppose that a war -is being carried on by a vast army, at the head of which there is a -very great commander. Now, this commander knows too well to expose -his person; in truth, he is never seen by any of his subordinates. He -remains at work in a well-guarded room, from which telegraphic wires -lead to the headquarters of the various divisions. He can thus, by -means of these wires, transmit his orders to the generals of these -divisions, and by the same means receive back information as to the -condition of each. - -Thus his headquarters become a centre, into which all information is -poured, and out of which all commands are issued. - -Now, that mysterious thing called life, about the nature of which we -know so little, is probably not unlike such a commander. Life is not -a bully, who swaggers out into the open universe, upsetting the laws -of energy in all directions, but rather a consummate strategist, who, -sitting in his secret chamber, before his wires, directs the movements -of a great army.[10] - -223. Let us next suppose that our imaginary army is in rapid march, and -let us try to find out the cause of this movement. We find that, in the -first place, orders to march have been issued to the troops under them -by the commanders of each regiment. In the next place, we learn that -staff officers, attached to the generals of the various divisions, have -conveyed these orders to the regimental commanders; and, finally, we -learn that the order to march has been telegraphed from headquarters to -these various generals. - -Descending now to ourselves, it is probably somewhere in the mysterious -and well-guarded brain-chamber that the delicate directive touch is -given which determines our movements. This chamber forms, as it were, -the headquarters of the general in command, who is so well withdrawn as -to be absolutely invisible to all his subordinates. - -224. Joule, Carpenter, and Mayer were at an early period aware of the -restrictions under which animals are placed by the laws of energy, -and in virtue of which the power of an animal, as far as energy is -concerned, is not creative, but only directive. It was seen that, in -order to do work, an animal must be fed; and, even at a still earlier -period, Count Rumford remarked that a ton of hay will be administered -more economically by feeding a horse with it, and then getting work out -of the horse, than by burning it as fuel in an engine. - -225. In this chapter, the same line of thought has been carried -out a little further. We have seen that life is associated with -delicately-constructed machines, so that whenever a transmutation of -energy is brought about by a living being, could we trace the event -back, we should find that the physical antecedent was probably a much -less transmutation, while again the antecedent of this would probably -be found still less, and so on, as far as we could trace it. - -226. But with all this, we do not pretend to have discovered the true -nature of life itself, or even the true nature of its relation to the -material universe. - -What we have ventured is the assertion that, as far as we can judge, -life is always associated with machinery of a certain kind, in virtue -of which an extremely delicate directive touch is ultimately magnified -into a very considerable transmutation of energy. Indeed, we can hardly -imagine the freedom of motion implied in life to exist apart from -machinery possessed of very great delicacy of construction. - -In fine, we have not succeeded in solving the problem as to the true -nature of life, but have only driven the difficulty into a borderland -of thick darkness, into which the light of knowledge has not yet been -able to penetrate. - - -_Organized Tissues are subject to Decay._ - -227. We have thus learned two things, for, in the first place, we -have learned that life is associated with delicacy of construction, -and in the next (Art. 220), that delicacy of construction implies -an unstable arrangement of natural forces. We have now to remark -that the particular force which is thus used by living beings is -chemical affinity. Our bodies are, in truth, examples of an unstable -arrangement of chemical forces, and the materials which composed them, -if not liable to sudden explosion, like fulminating powder, are yet -preeminently the subjects of decay. - -228. Now, this is more than a mere general statement; it is a truth -that admits of degrees, and in virtue of which those parts of our -bodies which have, during life, the noblest and most delicate office to -perform, are the very first to perish when life is extinct. - - “Oh! o’er the eye death most exerts his might, - And hurls the spirit from her throne of light; - Sinks those blue orbs in their long last eclipse, - But spares us yet the charm around the lips.” - -So speaks the poet, and we have here an aspect of things in which the -lament of the poet becomes the true interpretation of nature. - - -_Difference between Animals and Inanimate Machines._ - -229. We are now able to recognize the difference between the relations -to energy of a living being, such as man, and a machine, such as a -steam-engine. - -There are many points in common between the two. Both require to be -fed, and in both there is the transmutation of the energy of chemical -separation implied in fuel and food into that of heat and visible -motion. - -But while the one--the engine--requires for its maintenance only -carbon, or some other variety of chemical separation, the other--the -living being--demands to be supplied with organized tissue. In fact, -that delicacy of construction which is so essential to our well-being, -is not something which we can elaborate internally in our own -frames--all that we can do is to appropriate and assimilate that which -comes to us from without; it is already present in the food which we -eat. - - -_Ultimate Dependence of Life upon the Sun._ - -230. We have already (Art. 203) been led to recognize the sun as the -ultimate material source of all the energy which we possess, and we -must now regard him as the source likewise of all our delicacy of -construction. It requires the energy of his high temperature rays so to -wield and manipulate the powerful forces of chemical affinity; so to -balance these various forces against each other, as to produce in the -vegetable something which will afford our frames, not only energy, but -also delicacy of construction. - -Low temperature heat would be utterly unable to accomplish this; it -consists of ethereal vibrations which are not sufficiently rapid, and -of waves that are not sufficiently short, for the purpose of shaking -asunder the constituents of compound molecules. - -231. It thus appears that animals are, in more ways than one, -pensioners upon the sun’s bounty; and those instances, which at first -sight appear to be exceptions, will, if studied sufficiently, only -serve to confirm the rule. - -Thus the recent researches of Dr. Carpenter and Professor Wyville -Thomson have disclosed to us the existence of minute living beings in -the deepest parts of the ocean, into which we may be almost sure no -solar ray can penetrate. How, then, do these minute creatures obtain -that energy and delicacy of construction without which they cannot -live? in other words, how are they fed? - -Now, the same naturalists who discovered the existence of these -creatures, have recently furnished us with a very probable explanation -of the mystery. They think it highly probable that the whole ocean -contains in it organic matter to a very small but yet perceptible -extent, forming, as they express it, a sort of diluted soup, which thus -becomes the food of these minute creatures. - -232. In conclusion, we are dependent upon the sun and centre of our -system, not only for the mere energy of our frames, but also for our -delicacy of construction--the future of our race depends upon the sun’s -future. But we have seen that the sun must have had a beginning, and -that he will have an end. - -We are thus induced to generalize still further, and regard, not only -our own system, but the whole material universe when viewed with -respect to serviceable energy, as essentially evanescent, and as -embracing a succession of physical events which cannot go on for ever -as they are. - -But here at length we come to matters beyond our grasp; for physical -science cannot inform us what must have been before the beginning, nor -yet can it tell us what will take place after the end. - - -FOOTNOTES: - -[10] _See_ an article on “The Position of Life,” by the author of this -work, in conjunction with Mr. J. N. Lockyer, “Macmillan’s Magazine,” -September, 1868; also a lecture on “The Recent Developments of Cosmical -Physics,” by the author of this work. - - - - - APPENDIX. - - CORRELATION OF VITAL WITH CHEMICAL AND - PHYSICAL FORCES. - - BY JOSEPH LE CONTE, - - PROFESSOR OF GEOLOGY AND NATURAL HISTORY IN THE - UNIVERSITY OF CALIFORNIA. - - - - -CORRELATION OF VITAL WITH CHEMICAL AND PHYSICAL FORCES. - - -Vital force; whence is it derived? What is its relation to the other -forces of Nature? The answer of modern science to these questions is: -It is derived from the lower forces of Nature; it is related to other -forces much as these are related to each other--it is correlated with -chemical and physical forces. - -At one time matter was supposed to be destructible. By combustion or -by evaporation matter seemed to be consumed--to pass out of existence; -but now we know it only changes its form from the solid or liquid to -the gaseous condition--from the visible to the invisible--and that, -amid all these changes, the same quantity of matter remains. Creation -or destruction of matter, increase or diminution of matter, lies beyond -the domain of Science; her domain is confined entirely to the changes -of matter. Now, it is the doctrine of modern science that the same is -true of force. Force seems often to be annihilated. Two cannon-balls -of equal size and velocity meet each other and fall motionless. The -immense energy of these moving bodies seems to pass out of existence. -But not so; it is changed into heat, and the exact amount of heat may -be calculated; moreover, an equal amount of heat may be changed back -again into an equal amount of momentum. Here, therefore, force is not -lost, but is changed from a visible to an invisible form. Motion is -changed from bodily motion into molecular motion. Thus heat, light, -electricity, magnetism, chemical affinity, and mechanical force, are -transmutable into each other, back and forth; but, amid all these -changes, the amount of force remains unchanged. Force is incapable of -destruction, except by the same power which created it. The domain -of Science lies within the limits of these changes--creation and -annihilation lie outside of her domain. - -The mutual convertibility of forces into each other is called -_correlation of forces_; the persistence of the same amount, amid all -these protean forms, is called _conservation of force_.[11] - -The correlation of physical forces with each other and with chemical -force is now universally acknowledged and somewhat clearly conceived. -The correlation of vital force with these is not universally -acknowledged, and, where acknowledged, is only imperfectly conceived. -In 1859 I published a paper[12] in which I attempted to put the idea of -correlation of vital force with chemical and physical forces in a more -definite and scientific form. The views expressed in that paper have -been generally adopted by physiologists. Since the publication of the -paper referred to, the subject has lain in my mind, and grown at least -somewhat. I propose, therefore, now to reëmbody my views in a more -popular form, with such additions as have occurred to me since. - -There are four planes of material existence, which may be represented -as raised one above another. These are: 1. The plane of elementary -existence; 2. The plane of chemical compounds, or mineral kingdom; -3. The plane of vegetable existence; and, 4. The plane of animal -existence. Their relations to each other are truly expressed by writing -them one above the other, thus: - - I may sometimes use the word energy instead. If any one should charge - me with want of precision in language, my answer is: Our language - cannot be more precise until our ideas in this department are far - clearer than now. - - 4. _Animal Kingdom._ - 3. _Vegetable Kingdom._ - 2. _Mineral Kingdom._ - 1. _Elements._ - -Now, it is a remarkable fact that there is a special force, whose -function it is to raise matter from each plane to the plane above, -and to execute movements on the latter. Thus, it is the function -of chemical affinity alone to raise matter from No. 1 to No. 2, as -well as to execute all the movements, back and forth, by action and -reaction; in a word, to produce all the phenomena on No. 2 which -together constitute the science of chemistry. It is the prerogative -of vegetable life-force alone to lift matter from No. 2 to No. 3, as -well as to execute all the movements on that plane, which together -constitute the science of vegetable physiology. It is the prerogative -of animal life-force alone to lift matter from No. 3 to No. 4, and to -preside over the movements on this plane, which together constitute the -science of animal physiology. But there is no force in Nature capable -of raising matter at once from No. 1 to No. 3, or from No. 2 to No. 4, -without stopping and receiving an accession of force, of a different -kind, on the intermediate plane. Plants cannot feed upon elements, but -only on chemical compounds; animals cannot feed on minerals, but only -on vegetables. We shall see in the sequel that this is the necessary -result of the principle of conservation of force in vital phenomena. - -It is well known that atoms, in a nascent state--i. e., at the moment -of their separation from previous combination--are endowed with -peculiar and powerful affinity. Oxygen and nitrogen, nitrogen and -hydrogen, hydrogen and carbon, which show no affinity for each other -under ordinary circumstances, readily unite when one or both are in a -nascent condition. The reason seems to be that, when the elements of -a compound are torn asunder, the chemical affinity which previously -bound them together is set free, ready and eager to unite the nascent -elements with whatever they come in contact with. This state of exalted -chemical energy is retained but a little while, because it is liable -to be changed into some other form of force, probably heat, and is -therefore no longer chemical energy. To illustrate by the planes: -matter falling down from No. 2 to No. 1 generates force by which matter -is lifted from No. 1 to No. 2. Decomposition generates the force by -which combination is effected. This principle underlies every thing I -shall further say. - -There are, therefore, two ideas or principles underlying this paper: -1. The correlation of vital with physical and chemical forces; 2. -That in all cases _vital force is produced by decomposition_--is -transformed nascent affinity. Neither of these is new. Grove, many -years ago, brought out, in a vague manner, the idea that vital force -was correlated with chemical and physical forces.[13] In 1848 Dr. -Freke, M. R. I. A., of Dublin, first advanced the idea that vital force -of animal life was generated by decomposition. In 1851 the same idea -was brought out again by Dr. Watters, of St. Louis. These papers were -unknown to me when I wrote my article. They have been sent to me in the -last few years by their respective authors. Neither of these authors, -however, extends this principle to vegetation, the most fundamental -and most important phenomenon of life. In 1857 the same idea was again -brought out by Prof. Henry, of the Smithsonian Institution, and by him -extended to vegetation. I do not, therefore, now claim to have first -advanced this idea, but I do claim to have in some measure rescued it -from vagueness, and given it a clearer and more scientific form. - -I wish now to apply these principles in the explanation of the most -important phenomena of vegetable and animal life: - -1. VEGETATION.--The most important phenomenon in the life-history of -a plant--in fact, the starting-point of all life, both vegetable and -animal--is the formation of organic matter in the leaves. The necessary -conditions for this wonderful change of mineral into organic matter -seem to be, sunlight, chlorophyl, and living protoplasm, or bioplasm. -This is the phenomenon I wish now to discuss. - -The plastic matters of which vegetable structure is built are of -two kinds--amyloids and albuminoids. The amyloids, or starch and -sugar groups, consist of C, H, and O; the albuminoids of C, H, O, -N, and a little S and P. The quantity of sulphur and phosphorus is -very small, and we will neglect them in this discussion. The food -out of which these substances are elaborated are, CO₂, H₂O, -and H_{3}N--carbonic acid, water, and ammonia. Now, by the agency of -sunlight in the presence of chlorophyl and bioplasm, these chemical -compounds (CO₂, H₂O, and H_{3}N) are torn asunder, or shaken -asunder, or decomposed; the excess of O, or of O and H, is rejected, -and the remaining elements in a nascent condition combine to form -organic matter. To form the amyloids--starch, dextrine, sugar, -cellulose--only CO₂ and H₂O are decomposed, and excess of O -rejected. To form albuminoids, or protoplasm, CO₂, H₂O, and -H_{3}N, are decomposed, and excess of O and H rejected. - -It would seem in this case, therefore, that physical force (light) -is changed into nascent chemical force, and this nascent chemical -force, under the peculiar conditions present, forms organic matter, -and reappears as vital force. Light falling on living green leaves is -destroyed or consumed in doing the work of decomposition; disappears -as light, to reappear as nascent chemical energy; and this in its -turn disappears in forming organic matter, to reappear as the vital -force of the organic matter thus formed. The light which disappears is -proportioned to the O, or the O and H rejected; is proportioned also to -the quantity of organic matter formed, and also to the amount of vital -force resulting. To illustrate: In the case of amyloids, oxygen-excess -falling or running down from plane No. 2 to plane No. 1 generates force -to raise C, H, and O, from plane No. 2 to plane No. 3. In the case of -albuminoids, oxygen-excess and hydrogen-excess running down from No. 2 -to No. 1 generate force to raise C, H, O, and N, from No. 2 to No. 3. -To illustrate again: As sun-heat falling upon water disappears as heat, -to reappear as mechanical power, raising the water into the clouds, so -sunlight falling upon green leaves disappears as light, to reappear as -vital force lifting matter from the mineral into the organic kingdom. - -2. GERMINATION.--Growing plants, it is seen, take their life-force -from the sun; but seeds germinate and commence to grow in the dark. -Evidently there must be some other source from which they draw their -supply of force. They cannot draw force from the sun. This fact is -intimately connected with another fact, viz., that they do not draw -their food from the mineral kingdom. The seed in germination feeds -entirely upon a supply of organic matter laid up for it by the -mother-plant. It is the decomposition of this organic matter which -supplies the force of germination. Chemical compounds are comparatively -stable--it requires sunlight to tear them asunder; but organic matter -is more easily decomposed--it is almost spontaneously decomposed. -It may be that heat (a necessary condition of germination) is the -force which determines the decomposition. However this may be, it -is certain that a portion of the organic matter laid up in the seed -is decomposed, burned up, to form CO₂ and H₂O, and that this -combustion furnishes the force by which the mason-work of tissue-making -is accomplished. In other words, of the food laid up in the form of -starch, dextrine, protoplasm, a portion is decomposed to furnish the -force by which the remainder is organized. Hence the seed always loses -weight in germination; it cannot develop unless it is in part consumed; -“it is not quickened except it die.” This self-consumption continues -until the leaves and roots are formed; then it begins to draw force -from the sun, and food from the mineral kingdom. - -To illustrate: In germination, matter running down from plane No. 3 -to plane No. 2 generates force by which other similar matter is moved -about and raised to a somewhat higher position on plane No. 3. As -water raised by the sun may be stored in reservoirs, and in running -down from these may do work, so matter raised by sun-force into the -organic kingdom by one generation is stored as force to do the work of -germination of the next generation. Again, as, in water running through -an hydraulic ram, a portion runs to waste, in order to generate force -to lift the remainder to a higher level, so, of organic matter stored -in the seed, a portion runs to waste to create force to organize the -remainder. - -Thus, then, it will be seen that three things, viz., the absence -of sunlight, the use of organic food, and the loss of weight, are -indissolubly connected in germination, and all explained by the -principle of conservation of force. - -3. STARTING OF BUDS.--Deciduous trees are entirely destitute of leaves -during the winter. The buds must start to grow in the spring without -leaves, and therefore without drawing force from the sun. Hence, -also, food in the organic form must be, and is, laid up from the -previous year in the body of the tree. A portion of this is consumed -with the formation of CO₂ and H₂O, in order to create force for -the development of the buds. So soon as by this means the leaves are -formed, the plant begins to draw force from the sun, and food from the -mineral kingdom. - -4. PALE PLANTS.--Fungi and etiolated plants have no chlorophyl, -therefore cannot draw their force from the sun, nor make organic -matters from inorganic. Hence these also must feed on organic matter; -not, indeed, on starch, dextrine, and protoplasm, but on decaying -organic matter. In these plants the organic matter is taken up in some -form intermediate between the planes No. 3 and No. 2. The matter thus -taken up is, a portion of it, consumed with the formation of CO₂ and -H₂O, in order to create force necessary to organize the remainder. -To illustrate: Matter falling from some intermediate point between No. -2 and No. 3 to No. 2, produces force sufficient to raise matter from -the same intermediate point to No. 3; a portion runs to waste downward, -and creates force to push the remainder upward. - -5. GROWTH OF GREEN PLANTS AT NIGHT.--It is well known that almost all -plants grow at night as well as in the day. It is also known that -plants at night exhale CO₂. These two facts have not, however, as -far as I know, been connected with one another, and with the principle -of conservation of force. It is usually supposed that in the night -the decomposition of CO₂ and exhalation of oxygen are checked by -withdrawal of sun light, and some of the CO₂ in the ascending sap is -exhaled by a physical law. But this does not account for the growth. It -is evident that, in the absence of sun light, the force required for -the work of tissue-building can be derived only from the decomposition -and combustion of organic matter. There are two views as to the source -of this organic matter, either or both of which may be correct: First. -There seems to be no doubt that most plants, especially those grown in -soils rich in _humus_, take up a portion of their food in the form of -semi-organic matter, or soluble _humus_. The combustion of a portion of -this in every part of the plant, by means of oxygen also absorbed by -the roots, and the formation of CO₂, undoubtedly creates a supply of -force night and day, independently of sunlight. The force thus produced -by the combustion of a portion might be used to raise the remainder -into starch, dextrine, etc., or might be used in tissue-building. -During the day, the CO₂ thus produced would be again decomposed in -the leaves by sunlight, and thus create an additional supply of force. -During the night, the CO₂ would be exhaled.[14] - -Again: It is possible that more organic matter is made by sunlight -during the day than is used up in tissue-building. Some of this excess -is again consumed, and forms CO₂ and H₂O, in order to continue -the tissue-building process during the night. Thus the plant during the -day stores up sun-force sufficient to do its work during the night. -It has been suggested by Dr. J. C. Draper,[15] though not proved, or -even rendered probable, that the force of tissue-building (_force -plastique_) is always derived from decomposition, or combustion of -organic matter. In that case, the force of organic-matter formation -is derived from the sun, while the force of tissue-building (which is -relatively small) is derived from the combustion of organic matter thus -previously formed. - -6. FERMENTATION.--The plastic matters out of which vegetable tissue -is built, and which are formed by sunlight in the leaves, are of -two kinds, viz., amyloids (dextrine, sugar, starch, cellulose), and -albuminoids, or protoplasm. Now, the amyloids are comparatively -stable, and do not spontaneously decompose; but the albuminoids not -only decompose spontaneously themselves, but drag down the amyloids -with which they are associated into concurrent decomposition--not only -change themselves, but propagate a change into amyloids. Albuminoids, -in various stages and kinds of decomposition, are called ferments. The -propagated change in amyloids is called fermentation. By various kinds -of ferments, amyloids are thus dragged down step by step to the mineral -kingdom, viz., to CO₂ and H₂O. The accompanying table exhibits -the various stages of the descent of starch, and the ferments by which -they are effected: - - 1. Starch } - 2. Dextrine } Diastase. - 3. Sugar } - 4. Alcohol and CO₂ Yeast. - 5. Acetic acid Mother of vinegar. - 6. CO₂ and H₂O Mould. - -By appropriate means, the process of descent may be stopped on any one -of these planes. By far too much is, unfortunately, stopped on the -fourth plane. The manufacturer and chemist may determine the downward -change through all the planes, and the chemist has recently succeeded -in ascending again to No. 4; but the plant ascends and descends the -scale at pleasure (avoiding, however, the fourth and fifth), and even -passes at one step from the lowest to the highest. - -Now, it will be seen by the table that, connected with each of -these descensive changes, there is a peculiar ferment associated. -Diastase determines the change from starch to dextrine and -sugar--saccharification; yeast, the change from sugar to -alcohol--fermentation; mother of vinegar, the change from alcohol to -acetic acid--acetification; and a peculiar mould, the change from -acetic acid to CO₂ and water. But what is far more wonderful and -significant is, that, associated with each of these ferments, except -diastase, and therefore with each of these descensive changes, except -the change from starch to sugar, or saccharification, there is a -peculiar form of life. Associated with alcoholic fermentation, there -is the yeast-plant; with acetification, the vinegar-plant; and with the -decomposition of vinegar, a peculiar kind of mould. We will take the -one which is best understood, viz., yeast-plant (saccharomyce), and its -relation to alcoholic fermentation. - -It is well known that, in connection with alcoholic fermentation, -there is a peculiar unicelled plant which grows and multiplies. -Fermentation never takes place without the presence of this plant; this -plant never grows without producing fermentation, and the rapidity -of the fermentation is in exact proportion to the rapidity of the -growth of the plant. But, as far as I know, the fact has not been -distinctly brought out that the decomposition of the sugar into alcohol -and carbonic acid furnishes the force by which the plant grows and -multiplies. If the growing cells of the yeast-plant be observed under -the microscope, it will be seen that the carbonic-acid bubbles form, -and therefore probably the decomposition of sugar takes place only in -contact with the surface of the yeast-cells. The yeast-plant not only -assimilates matter, but also force. It decomposes the sugar in order -that it may assimilate the chemical force set free. - -We have already said that the change from starch to sugar, determined -by diastase (saccharification), is the only one in connection with -which there is no life. Now, it is a most significant fact, in this -connection, that this is also the only change which is not, in a proper -sense, descensive, or, at least, where there is no decomposition. - -We now pass from the phenomena of vegetable to the phenomena of animal -life. - -7. DEVELOPMENT OF THE EGG IN INCUBATION.--The development of the egg -in incubation is very similar to the germination of a seed. An egg -consists of albuminous and fatty matters, so inclosed that, while -oxygen of the air is admitted, nutrient matters are excluded. During -incubation the egg changes into an embryo; it passes from an almost -unorganized to a highly-organized condition, from a lower to a higher -condition. There is work done: there must be expenditure of force; -but, as we have already seen, vital force is always derived from -decomposition. But, as the matters to be decomposed are not taken _ab -extra_, the egg must consume itself; that it does so, is proved by -the fact that in incubation the egg absorbs oxygen, eliminates CO₂ -and probably H₂O, and loses weight. As in the seed, a portion of -the matters contained in the egg is consumed in order to create force -to organize the remainder. Matter runs down from plane No. 4 to plane -No. 2, and generates force to do the work of organization on plane No. -4. The amount of CO₂ and H₂O formed, and therefore the loss of -weight, is a measure of the amount of plastic work done. - -8. DEVELOPMENT WITHIN THE CHRYSALIS SHELL.--It is well known that many -insects emerge from the egg not in their final form, but in a wormlike -form, called a larva. After this they pass into a second passive state, -in which they are again covered with a kind of shell--a sort of second -egg-state, called the chrysalis. From this they again emerge as the -perfect insect. The butterfly is the most familiar, as well as the -best, illustration of these changes. The larva or caterpillar eats with -enormous voracity, and grows very rapidly. When its growth is complete, -it covers itself with a shell, and remains perfectly passive and almost -immovable for many days or weeks. During this period of quiescence of -animal functions there are, however, the most important changes going -on within. The wings and legs are formed, the muscles are aggregated in -bundles for moving these appendages, the nervous system is more highly -developed, the mouth-organs and alimentary canal are greatly changed -and more highly organized, the simple eyes are changed into compound -eyes. Now, all this requires expenditure of force, and therefore -decomposition of matter; but no food is taken, therefore the chrysalis -must consume its own substance, and therefore lose weight. It does so; -the weight of the emerging butterfly is in many cases not one-tenth -that of the caterpillar. Force is stored up in the form of organic -matter only to be consumed in doing plastic work. - -9. MATURE ANIMALS.--Whence do animals derive their vital force? I -answer, from the decomposition of their food and the decomposition of -their tissues. - -Plants, as we have seen, derive their vital force from the -decomposition of their mineral food. But the chemical compounds on -which plants feed are very stable. Their decomposition requires a -peculiar and complex contrivance for the reception and utilization of -sunlight. These conditions are wanting in animals. Animals, therefore, -cannot feed on chemical compounds of the mineral kingdom; they must -have organic food which easily runs into decomposition; they must feed -on the vegetable kingdom. - -Animals are distinguished from vegetables by incessant decay in -every tissue--a decay which is proportional to animal activity. This -incessant decay necessitates incessant repair, so that the animal body -has been likened to a temple on which two opposite forces are at work -in every part, the one tearing down, the other repairing the breach as -fast as made. In vegetables no such incessant decay has ever been made -out. If it exists, it must be very trifling in comparison. Protoplasm, -it is true, is taken up from the older parts of vegetables, and these -parts die; but the protoplasm does not seem to decompose, but is used -again for tissue-building. Thus the internal activity of animals is of -two kinds, tissue-destroying and tissue-building; while that of plants -seems to be, principally, at least, of one kind, tissue-building. -Animals use food for force and repair and growth, and in the mature -animal only for force and repair. Plants, except in reproduction, use -food almost wholly for growth--they never stop growing. - -Now, the food of animals is of two kinds, amyloids and albuminoids. The -carnivora feed entirely on albuminoids; herbivora on both amyloids and -albuminoids. All this food comes from the vegetable kingdom, directly -in the case of herbivora, indirectly in the case of carnivora. Animals -cannot make organic matter. Now, the tissues of animals are wholly -albuminoid. It is obvious, therefore, that for the repair of the -tissues the food must be albuminoid. The amyloid food, therefore (and, -as we shall see in carnivora, much of the albuminoid), must be used -wholly for force. As coal or wood, burned in a steam-engine, changes -chemical into mechanical energy, so food, in excess of what is used -for repair, is burned up to produce animal activity. Let us trace more -accurately the origin of animal force by examples. - -10. CARNIVORA.--The food of carnivora is entirely albuminoid. The idea -of the older physiologists, in regard to the use of this food, seems -to have been as follows: Albuminoid matter is exceedingly unstable; it -is matter raised, with much difficulty and against chemical forces, -high, and delicately balanced on a pinnacle, in a state of unstable -equilibrium, for a brief time, and then rushes down again into the -mineral kingdom. The animal tissues, being formed of albuminoid matter, -are short-lived; the parts are constantly dying and decomposing; the -law of death necessitates the law of reproduction; decomposition -necessitates repair, and therefore food for repair. But the force by -which repair is effected was for them, and for many physiologists now, -underived, innate. But the doctrine maintained by me in the paper -referred to is, that the decomposition of the tissues creates not only -the necessity, but also the force, of repair. - -Suppose, in the first place, a carnivorous animal uses just enough -food to repair the tissues, and no more--say an ounce. Then I say the -ounce of tissue decayed not only necessitates the ounce of albuminous -food for repair, but the decomposition sets free the force by which -the repair is effected. But it will be perhaps objected that the force -would all be consumed in repair, and none left for animal activity of -all kinds. I answer: it would not all be used up in repair, for, the -food being already albuminoid, there is probably little expenditure of -force necessary to change it into tissue; while, on the other hand, the -force generated by the decomposition of tissue into CO₂, H₂O, -and urea, is very great--the ascensive change is small, the descensive -change is great. The decomposition of one ounce of albuminous tissue -into CO₂, H₂O, and urea, would therefore create force sufficient -not only to change one ounce of albuminous matter into tissue, but -also leave a considerable amount for animal activities of all kinds. A -certain quantity of matter, running down from plane No. 4 to plane No. -2, creates force enough not only to move the same quantity of matter -about on plane No. 4, but also to do much other work besides. It is -probable, however, that the wants of animal activity are so immediate -and urgent that, under these conditions, much food would be burned for -this purpose, and would not reach the tissues, and the tissues would be -imperfectly repaired, and would therefore waste. - -Take, next, the carnivorous animal full fed. In this case there can -be no doubt that, while a portion of the food goes to repair the -tissues, by far the larger portion is consumed in the blood, and -passes away partly as CO₂ and H₂O through the lungs, and partly -as urea through the kidneys. This part is used, and can be of use -only, to create force. The food of carnivora, therefore, goes partly -to tissue-building, and partly to create heat and force. The force of -carnivorous animals is derived partly from decomposing tissues and -partly from food-excess consumed in the blood. - -11. HERBIVORA.--The food of herbivora and of man is mixed--partly -albuminoid and partly amyloid. In man, doubtless, the albuminoids -are usually in excess of what is required for tissue-building; but -in herbivora, probably, the albuminoids are not in excess of the -requirements of the decomposing tissues. In this case, therefore, the -whole of the albuminoids is used for tissue-making, and the whole of -the amyloids for force-making. In this class, therefore, these two -classes of food may be called tissue-food and force-food. The force of -these animals, therefore, is derived partly from the decomposition of -the tissues, but principally from the decomposition and combustion of -the amyloids and fats. - -Some physiologists speak of the amyloid and fat food as being burned -to keep up the animal heat; but it is evident that the prime object -in the body, as in the steam-engine, is not heat, but force. Heat is -a mere condition and perhaps a necessary concomitant of the change, -but evidently not the prime object. In tropical regions the heat is -not wanted. In the steam-engine, chemical energy is first changed into -heat, and heat into mechanical energy; in the body the change is, -probably, much of it direct, and not through the intermediation of heat. - -12. We see at once, from the above, why it is that plants cannot feed -on elements, viz., because their food must be decomposed in order to -create the organic matter out of which all organisms are built. This -elevation of matter, which takes place in the green leaves of plants, -is the starting-point of life; upon it alone is based the possibility -of the existence of the organic kingdom. The running down of the -matter there raised determines the vital phenomena of germination, of -pale plants, and even of some of the vital phenomena of green plants, -and all the vital phenomena of the animal kingdom. The stability of -chemical compounds, usable as plant-food, is such that a peculiar -contrivance and peculiar conditions found only in the green leaves of -plants are necessary for their decomposition. We see, therefore, also, -why animals as well as pale plants cannot feed on mineral matter. - -We easily see also why the animal activity of carnivora is greater -than that of herbivora, for the amount of force necessary for the -assimilation of their albuminoid food is small, and therefore a larger -amount is left over for animal activity. Their food is already on plane -No. 4; assimilation, therefore, is little more than a _shifting_ on the -plane No. 4 from a liquid to a solid condition--from liquid albuminoid -of the blood to solid albuminoid of the tissues. - -We see also why the internal activity of plants may conceivably be -only of one kind; for, drawing their force from the sun, tissue-making -is not necessarily dependent on tissue-decay. While, on the other -hand, the internal activity of animals must be of two kinds, decay and -repair; for animals always draw a portion of their force, and starving -animals the whole of their force, from decaying tissue. - -13. There are several general thoughts suggested by this subject, which -I wish to present in conclusion: - -_a._ We have said there are four planes of matter raised one above the -other: 1. Elements; 2. Chemical compounds; 3. Vegetables; 4. Animals. -Their relative position is truly represented thus: - - 4. _Animals._ - 3. _Plants._ - 2. _Chemical compounds._ - 1. _Elements._ - -Now, there are also four planes of force similarly related to each -other, viz., physical force, chemical force, vitality, and will. On the -first plane of matter operates physical force only; for chemical force -immediately raises matter into the second plane. On the second plane -operates, in addition to physical, also chemical force. On the third -plane operates, in addition to physical and chemical, also vital force. -On the fourth plane, in addition to physical, chemical, and vital, -also the force characteristic of animals, viz., will.[16] With each -elevation there is a peculiar force added to the already existing, -and a peculiar group of phenomena is the result. As matter only rises -step by step from plane to plane, and never two steps at a time, so -also force, in its transformation into higher forms of force, rises -only step by step. Physical force does not become vital except through -chemical force, and chemical force does not become will except through -vital force. - -Again, we have compared the various grades of matter, not to a -gradually rising inclined plane, but to successive planes raised one -above the other. There are, no doubt, some intermediate conditions; -but, as a broad, general fact, the changes from plane to plane are -sudden. Now, the same is true also of the forces operating on these -planes--of the different grades of force, and their corresponding -groups of phenomena. The change from one grade to another, as from -physical to chemical, or from chemical to vital, is not, as far as we -can see, by sliding scale, but suddenly. The groups of phenomena which -we call physical, chemical, vital, animal, rational, and moral, do not -merge into each other by insensible gradations. In the ascensive scale -of forces, in the evolution of the higher forces from the lower, there -are places of rapid, paroxysmal change. - -_b._ Vital force is transformed into physical and chemical forces; but -it is not on that account identical with physical and chemical force, -and therefore we ought not, as some would have us, discard the term -vital force. There are two opposite errors on this subject: one is the -old error of regarding vital force as something innate, underived, -having no relation to the other forces of Nature; the other is the -new error of regarding the forces of the living body as nothing but -ordinary physical and chemical forces, and therefore insisting that -the use of the term vital force is absurd and injurious to science. -The old error is still prevalent in the popular mind, and still -haunts the minds of many physiologists; the new error is apparently -a revulsion from the other, and is therefore common among the most -advanced scientific minds. There are many of the best scientists who -ridicule the use of the term vital force, or vitality, as a remnant -of superstition; and yet the same men use the words gravity, magnetic -force, chemical force, physical force, etc. Vital force is not -underived--is not unrelated to other forces--is, in fact, correlated -with them; but it is nevertheless a distinct form of force, far more -distinct than any other form, unless it be still higher forms, and -therefore better entitled to a distinct name than any lower form. Each -form of force gives rise to a peculiar group of phenomena, and the -study of these to a peculiar department of science. Now, the group of -phenomena called vital is more peculiar, and more different from other -groups, than these are from each other; and the science of physiology -is a more distinct department than either physics or chemistry; and -therefore the form of force which determines these phenomena is more -distinct, and better entitled to a distinct name, than either physical -or chemical forces. De Candolle, in a recent paper,[17] suggests the -term vital movement instead of vital force; but can we conceive of -movement without force? And, if the movement is peculiar, so also is -the form of force. - -_c._ Vital is transformed physical and chemical forces; true, but the -necessary and very peculiar condition of this transformation is the -previous existence then and there of living matter. There is something -so wonderful in this peculiarity of vital force that I must dwell on it -a little. - -Elements brought in contact with each other under certain physical -conditions--perhaps heat or electricity--unite and rise into the second -plane, i. e., of chemical compounds; so also several elements, C, H, O, -and N, etc., brought in contact with each other under certain physical -or chemical conditions, such as light, nascency, etc., unite and rise -into plane No. 3, i. e., form organic matter. In both cases there is -chemical union under certain physical conditions; but in the latter -there is one unique condition, viz., the previous existence then and -there of organic matter, under the guidance of which the transformation -of matter takes place. In a word, organic matter is necessary -to produce organic matter; there is here a law of like producing -like--there is an assimilation of matter. - -Again, physical force changes into other forms of physical force, -or into chemical force, under certain physical conditions; so also -physical and chemical forces are changed into vital force under certain -physical conditions. But, in addition, there is one altogether unique -condition of the latter change, viz., the previous existence then and -there of vital force. Here, again, like produces like--here, again, -there is assimilation of force. - -This law of like producing like--this law of assimilation of matter -and force--runs throughout all vital phenomena, even to the minutest -details. It is a universal law of generation, and determines the -existence of species; it is the law of formation of organic matter and -organic force; it determines all the varieties of organic matter which -we call tissues and organs, and all the varieties of organic force -which we call functions. The same nutrient pabulum, endowed with the -same properties and powers, carried to all parts of a complex organism -by this wonderful law of like producing like, is changed into the -most various forms and endowed with the most various powers. There -are certainly limits and exceptions to this law, however; otherwise -differentiation of tissues, organs, and functions, could not take -place in embryonic development; but the limits and exceptions are -themselves subject to a law even more wonderful than the law of like -producing like itself, viz., the law of evolution. There is in all -organic nature, whether organic kingdom, organic individual, or organic -tissues, a law of variation, strongest in the early stages, limited -very strictly by another law--the law of inheritance, of like producing -like. - -_d._ We have seen that all development takes place at the expense of -decay--all elevation of one thing, in one place, at the expense of -corresponding running down of something else in another place. Force is -only transferred and transformed. The plant draws its force from the -sun, and therefore what the plant gains the sun loses. Animals draw -from plants, and therefore what the animal kingdom gains the vegetable -kingdom loses. Again, an egg, a seed, or a chrysalis, developing to a -higher condition, and yet taking nothing _ab extra_, must lose weight. -Some part must run down, in order that the remainder should be raised -to a higher condition. The amount of evolution is measured by the loss -of weight. By the law of conservation of force, it is inconceivable -that it should be otherwise. Evidently, therefore, in the universe, -taken as a whole, evolution of one part must be at the expense of -some other part. The evolution or development of the whole cosmos--of -the whole universe of matter--as a unit, by forces within itself, -according to the doctrine of conservation of force, is inconceivable. -If there be any such evolution, at all comparable with any known form -of evolution, it can only take place by a constant increase of the -whole sum of energy, i. e., by a constant influx of divine energy--for -the same quantity of matter in a higher condition must embody a greater -amount of energy. - -_e._ Finally, as organic matter is so much matter taken from the -common fund of matter of earth and air, embodied for a brief space, -to be again by death and decomposition returned to that common fund, -so also it would seem that the organic forces of the living bodies of -plants and animals may be regarded as so much force drawn from the -common fund of physical and chemical forces, to be again all refunded -by death and decomposition. Yes, by decomposition; we can understand -this. But death! can we detect any thing returned by simple death? -What is the nature of the difference between the living organism and -a dead organism? We can detect none, physical or chemical. All the -physical and chemical forces withdrawn from the common fund of Nature, -and embodied in the living organism, seem to be still embodied in the -dead until little by little it is returned by decomposition. Yet the -difference is immense, is inconceivably great. What is the nature of -this difference expressed in the formula of material science? What is -it that is gone, and whither is it gone? There is something here which -science cannot yet understand. Yet it is just this loss which takes -place in death, and before decomposition, which is in the highest sense -vital force. - -Let no one from the above views, or from similar views expressed by -others, draw hasty conclusions in favor of a pure materialism. Force -and matter, or spirit and matter, or God and Nature, these are the -opposite poles of philosophy--they are the opposite poles of thought. -There is no clear thinking without them. Not only religion and virtue, -but science and philosophy, cannot even exist without them. The belief -in spirit, like the belief in matter, rests on its own basis of -phenomena. The true domain of philosophy is to reconcile these with -each other. - - -FOOTNOTES: - -[11] In recent works the word _energy_ is used to designate active or -working force as distinguished from passive or non-working force. It is -in this working condition only that force is conserved, and therefore -_conservation of energy_ is the proper expression. Nevertheless, since -the distinction between force and energy is imperfectly or not at all -defined in the higher forms of force, and especially in the domain of -life, I have preferred in this article to use the word _force_ in the -general sense usual until recently. - -[12] _American Journal of Science_, November, 1859. _Philadelphia -Magazine_, vol. xix., p. 133. - -[13] In 1845 Dr. J. R. Mayer published a paper on “Organic Motion and -Nutrition.” I have not seen it. - -[14] For more full account, see my paper, _American Journal of -Science_, November, 1859, sixth and seventh heads. - -[15] _American Journal of Science_, November, 1872. The experiments -of Dr. Draper are inconclusive, because they are made on _seedlings_, -which, until their supply of organic food is exhausted, are independent -of sunlight. - -[16] I might add still another plane and another force, viz., the human -plane, on which operate, in addition to all the lower forces, also -free-will and reason. I do not speak of these, only because they lie -beyond the present ken of inductive science. - -[17] _Archives des Sciences_, vol. xlv., p. 345, December, 1872. - - - - -CORRELATION OF NERVOUS AND MENTAL FORCES. - -BY ALEXANDER BAIN, LL. D., - -PROFESSOR OF LOGIC AND MENTAL PHILOSOPHY IN THE UNIVERSITY OF -ABERDEEN. - - - - -THE CORRELATION OF NERVOUS AND MENTAL FORCES. - - -The doctrine called the correlation, persistence, equivalence, -transmutability, indestructibility of force, or the conservation of -energy, is a generality of such compass that no single form of words -seems capable of fully expressing it; and different persons may prefer -different statements of it. My understanding of the doctrine is, that -there are five chief powers or forces in Nature: one _mechanical_, -or _molar_, the momentum of moving matter; the others _molecular_, -or embodied in the molecules, also supposed in motion--these are, -heat, light, chemical force, electricity. To these powers, which are -unquestionable and distinct, it is usual to add vital force, of which, -however, it is difficult to speak as a whole; but one member of our -vital energies, the nerve-force, allied to electricity, fully deserves -to rank in the correlation. - -Taking the one mechanical force, and those three of the molecular -named heat, chemical force, electricity, there has now been established -a definite rate of commutation, or exchange, when any one passes into -any other. The mechanical equivalent of heat, the 772 foot-pounds of -Joule, expresses the rate of exchange between mechanical momentum -and heat: the equivalent or exchange of heat and chemical force is -given (through the researches of Andrews and others) in the figures -expressing the heat of combinations; for example, one pound of carbon -burnt evolves heat enough to raise 8,080 pounds of water one degree, C. -The combination of these to equivalents would show that the consumption -of half a pound of carbon would raise a man of average weight to the -highest summit of the Himalayas. - -It is an essential part of the doctrine, that force is never absolutely -created, and never absolutely destroyed, but merely transmuted in form -or manifestation. - -As applied to living bodies, the following are the usual positions. In -the growth of plants, the forces of the solar ray--heat and light--are -expended in decomposing (or deoxidizing) carbonic acid and water, and -in building up the living tissues from the liberated carbon and the -other elements; all which force is given up when these tissues are -consumed, either as fuel in ordinary combustion, or as food in animal -combustion. - -It is this animal combustion of the matter of plants, and of animals -(fed on plants)--namely, the reoxidation of carbon, hydrogen, -etc.--that yields all the manifestations of power in the animal frame. -And, in particular, it maintains (1) a certain warmth or temperature -of the whole mass, against the cooling power of surrounding space; it -maintains (2) mechanical energy, as muscular power; and it maintains -(3) nervous power, or a certain flow of the influence circulating -through the nerves, which circulation of influence, besides reacting -on the other animal processes--muscular, glandular, etc.--has for its -distinguishing concomitant the MIND. - -The extension of the correlation of force to mind, if at all competent, -must be made through the nerve-force, a genuine member of the -correlated group. Very serious difficulties beset the proposal, but -they are not insuperable. - -The history of the doctrines relating to mind, as connected with body, -is in the highest degree curious and instructive, but, for the purpose -of the present paper, we shall notice only certain leading stages of -the speculation.[18] - -Not the least important position is the Aristotelian; a position -in some respects sounder than what followed and grew out of it. In -Aristotle, we have a kind of gradation from the life of plants to the -highest form of human intelligence. In the following diagram, the -continuous lines may represent the material substance, and the dotted -lines the immaterial: - - - A. _Soul of Plants._ - - ---- Without consciousness. - - - B. _Animal Soul._ - - ---- Body and mind inseparable. - .... - - - C. _Human Soul_--NOUS--_Intellect_. - - I. Passive intellect. - - ---- Body and mind inseparable. - .... - - II. Active intellect--cognition of the highest principles. - - .... Pure form; detached from matter; the prime mover of all; immortal. - -All the phases of life and mind are inseparably interwoven with the -body (which inseparability is Aristotle’s definition of the soul) -except the last, the active _nous_, or intellect, which is detached -from corporeal matter, self-subsisting, the essence of Deity, and an -immortal substance, although the immortality is not personal to the -individual. (The immateriality of this higher intellectual agent was -net, however, that thorough-going negation of all material attributes -which we now understand by the word “immaterial.”) How such a -self-subsisting and purely spiritual soul could hold communication with -the body-leagued souls, Aristotle was at a loss to say--the difficulty -reappeared after him, and has never been got over. That there should -be an agency totally apart from, and entirely transcending, any known -powers of inert matter, involves no difficulty--for who is to limit -the possibilities of existence? The perplexity arises only when this -radically new and superior principle is made to be, as it were, off -and on with the material principle; performing some of its functions -in pure isolation, and others of an analogous kind by the aid of the -lower principle. The difference between the active and the passive -reason of Aristotle is a mere difference of gradation; the supporting -agencies assumed by him are a total contrast in kind--wide as the poles -asunder. There is no breach of continuity in the phenomena, there is an -impassable chasm between their respective foundations. - -Fifteen centuries after Aristotle, we reach what may be called the -modern settlement of the relations of mind and body, effected by Thomas -Aquinas. He extended the domain of the independent immaterial principle -from the highest intellectual soul of Aristotle to all the three souls -recognized by him--the vegetable or plant soul (without consciousness), -the animal soul (with consciousness), and the intellect throughout. The -two lower souls--the vegetable and the animal--need the coöperation of -the body in this life; the intellect works without any bodily organ, -except that it makes use of the perceptions of the senses. - - - A. _Vegetable or Nutritive Soul._ - - ---- Incorporates an immaterial part, although unconscious. - .... - - - B. _Animal Soul._ - - ---- Has an immaterial part, with consciousness. - .... - - - C. _Intellect._ - - .... Purely immaterial. - -The animal soul, B, contains sensation, appetite, and emotion, and is a -mixed or two-sided entity; but the intellect, C, is a purely one-sided -entity, the immaterial. This does not relieve our perplexities; the -phenomena are still generically allied and continuous--sensation passes -into intellect without any breach of continuity; but as regards the -agencies, the transition from a mixed or united material and immaterial -substance to an immaterial substance apart, is a transition to a -differently constituted world, to a transcendental sphere of existence. - -The settlement of Aquinas governed all the schools and all the -religious creeds, until quite recent times; it is, for example, -substantially the view of Bishop Butler. At the instance of modern -physiology, however, it has undergone modifications. The dependence -of purely intellectual operations, as memory, upon the material -processes, has been reluctantly admitted by the partisans of an -immaterial principle; an admission incompatible with the isolation of -the intellect in Aristotle and in Aquinas. This more thorough-going -connection of the mental and the physical has led to a new form of -expressing the relationship, which is nearer the truth, without being, -in my judgment, quite accurate. It is now often said _the mind and the -body act upon each other_; that neither is allowed, so to speak, to -pursue its course alone--there is a constant interference, a mutual -influence between the two. This view is liable to the following -objections: - -1. In the first place, it assumes that we are entitled to speak of -mind apart from body, and to affirm its powers and properties in that -separate capacity. But of mind apart from body we have no direct -experience, and absolutely no knowledge. The wind may act upon the sea, -and the waves may react upon the wind; but the agents are known in -separation--they are seen to exist apart before the shock of collision; -but we are not permitted to see a mind acting apart from its material -companion. - -2. In the second place, we have every reason for believing that there -is an unbroken material succession, side by side with all our mental -processes. From the ingress of a sensation, to the outgoing responses -in action, the mental succession is not for an instant dissevered from -a physical succession. A new prospect bursts upon the view; there is a -mental result of sensations, emotion, thought, terminating in outward -displays of speech or gesture. Parallel to this mental series is the -physical series of facts, the successive agitation of the physical -organs, called the eye, the retina, the optic nerve, optic centres, -cerebral hemispheres, outgoing nerves, muscles, etc. There is an -unbroken physical circle of effects, maintained while we go the round -of the mental circle of sensation, emotion, and thought. It would be -incompatible with every thing we know of the cerebral action to suppose -that the physical chain ends abruptly in a physical void, occupied by -an immaterial substance; which immaterial substance, after working -alone, imparts its results to the other edge of the physical break, -and determines the active response--two shores of the material with an -intervening ocean of the immaterial. There is, in fact, no rupture of -nervous continuity. The only tenable supposition is, that mental and -physical proceed together, as individual twins. When, therefore, we -speak of a mental cause, a mental agency, we have always a two-sided -cause; the effect produced is not the effect of mind alone, but of mind -in company with body. That mind should have operated on the body, is -as much as to say that a two-sided phenomenon, one side being bodily, -can influence the body; it is, after all, body acting upon body. When -a shock of fear paralyzes digestion, it is not the emotion of fear, -in the abstract, or as a pure mental existence, that does the harm; -it is the emotion in company with a peculiarly excited condition of -the brain and nervous system; and it is this condition of the brain -that deranges the stomach. When physical nourishment, or physical -stimulant, acting through the blood, quiets the mental irritation, and -restores a cheerful tone, it is not a bodily fact causing a mental -fact by a direct line of causation: the nourishment and the stimulus -determine the circulation of blood to the brain, give a new direction -to the nerve-currents, and the mental condition corresponding to -this particular mode of cerebral action henceforth manifests itself. -The line of mental sequence is thus, not mind causing body, and body -causing mind, but mind-body giving birth to mind-body; a much more -intelligible position. For this double or conjoint causation, we can -produce evidence; for the single-handed causation we have no evidence. - -If it were not my peculiar province to endeavor to clear up the -specially metaphysical difficulties of the relationship of mind and -body, I would pass over what is to me the most puzzling circumstance of -the relationship, and indeed the only real difficulty in the question. - -I say the real difficulty, for factitious difficulties in abundance -have been made out of the subject. It is made a mystery how mental -functions and bodily functions should be allied together at all. That, -however, is no business of ours; we accept this alliance, as we do any -other alliance, such as gravity with inert matter, or light with heat. -As a fact of the universe, the union is, properly speaking, just as -acceptable, and as intelligible, as the separation would be, if that -were the fact. The real difficulty is quite another thing. - -What I have in view is this: when I speak of mind as allied with -body--with a brain and its nerve-currents--I can scarcely avoid -_localizing_ the mind, giving it a local habitation. I am thereupon -asked to explain what always puzzled the schoolmen, namely, whether the -mind is all in every part, or only all in the whole; whether in tapping -any point I may come at consciousness, or whether the whole mechanism -is wanted for the smallest portion of consciousness. One might perhaps -turn the question by the analogy of the telegraph wire, or the electric -circuit, and say that a complete circle of action is necessary to any -mental manifestation; which is probably true. But this does not meet -the case. The fact is that, all this time we are speaking of nerves -and wires, we are not speaking of mind, properly so called, at all; we -are putting forward physical facts that go along with it, but these -physical facts are not the mental fact, and they even preclude us from -thinking of the mental fact. We are in this fix: mental states and -bodily states are utterly contrasted; they cannot be compared, they -have nothing in common except the most general of all attributes, -degree, and order in time; when engaged with one we must be oblivious -of all that distinguishes the other. When I am studying a brain -and nerve communicating, I am engrossed with properties exclusively -belonging to the object or material world; I am at that moment (except -by very rapid transitions or alternations) unable to conceive a truly -mental fact, my truly mental consciousness. Our mental experience, our -feelings and thoughts, have no extension, no place, no form or outline, -no mechanical division of parts; and we are incapable of attending to -any thing mental until we shut off the view of all that. Walking in the -country in spring, our mind is occupied with the foliage, the bloom, -and the grassy meads, all purely objective things; we are suddenly and -strongly arrested by the odor of the May-blossom; we give way for a -moment to the sensation of sweetness: for that moment the objective -regards cease; we think of nothing extended; we are in a state where -extension has no footing; there is, to us, place no longer. Such states -are of short duration, mere fits, glimpses; they are constantly shifted -and alternated with object states, but while they last and have their -full power we are in a different world; the material world is blotted -out, eclipsed, for the instant unthinkable. These subject-moments are -studied to advantage in bursts of intense pleasure, or intense pain, in -fits of engrossed reflection, especially reflection upon mental facts; -but they are seldom sustained in purity beyond a very short interval; -we are constantly returning to the object-side of things--to the world -where extension and place have their being. - -This, then, as it appears to me, is the only real difficulty of the -physical and mental relationship. There is an alliance with matter, -with the object, or extended world; but the thing allied, the mind -proper, has itself no extension, and cannot be joined in local union. -Now, we have no form of language, no familiar analogy, suited to this -unique conjunction; in comparison with all ordinary unions, it is a -paradox or a contradiction. We understand union in the sense of local -connection; here is a union where local connection is irrelevant, -unsuitable, contradictory, for we cannot think of mind without putting -ourselves out of the world of place. When, as in pure feeling--pleasure -or pain--we change to the subject attitude from the object attitude, -we have undergone a change not to be expressed by place; the fact is -not properly described by the transition from the _external_ to the -_internal_, for that is still a change in the region of the extended. -The only adequate expression is a _change of state_: a change from the -state of the extended cognition to a state of unextended cognition. -By various theologians, heaven has been spoken of us not a place, -but a _state_; and this is the only phrase that I can find suitable -to describe the vast, though familiar and easy, transition from the -material or extended, to the immaterial or unextended side of the -universe of being. - -When, therefore, we talk of incorporating mind with brain, we must be -held as speaking under an important reserve or qualification. Asserting -the union in the strongest manner, we must yet deprive it of the almost -invincible association of union in place. An extended organism is the -condition of our passing into a state where there is no extension. A -human being is an extended and material thing, attached to which is the -power of becoming alive to feeling and thought, the extreme remove from -all that is material; a condition of _trance_ wherein, while it lasts, -the material drops out of view--so much so, that we have not the power -to represent the two extremes as lying side by side, as container and -contained, or in any other mode of local conjunction. The condition -of our existing thoroughly in the one, is the momentary eclipse or -extinction of the other. - -The only mode of union that is not contradictory is the union of close -succession in _time_; or of position in a continued thread of conscious -life. We are entitled to say that the same being is, by alternate fits, -object and subject, under extended and under unextended consciousness; -and that without the extended consciousness the unextended would not -arise. Without certain peculiar modes of the extended--what we call -a cerebral organization, and so on--we could not have those times of -trance, our pleasures, our pains, and our ideas, which at present we -undergo fitfully and alternately with our extended consciousness. - -Having thus called attention to the metaphysical difficulty of -assigning the relative position of mind and matter, I will now state -briefly what I think the mode of dealing with mind in correlation with -the other forces. That there is a definite equivalence between mental -manifestations and physical forces, the same as between the physical -forces themselves, is, I think, conformable to all the facts, although -liable to peculiar difficulties in the way of decisive proof: - -I. The mental manifestations are in exact proportion to their physical -supports. - -If the doctrine of the thorough-going connection of mind and body -is good for any thing, it must go this length. There must be a -numerically-proportioned rise and fall of the two together. I believe -that all the unequivocal facts bear out this proportion. - -Take first the more obvious illustrations. In the employment of -external agents, as warmth and food, all will admit that the sensation -rises exactly as the stimulant rises, until a certain point is reached, -when the agency changes its character; too great heat destroying the -tissues, and too much food impeding digestion. There is, although we -may not have the power to fix it, a _sensational equivalent_ of heat, -of food, of exercise, of sound, of light; there is a definite change -of feeling, an accession of pleasure or of pain, corresponding to a -rise of temperature in the air of 10°, 20°, or 30°. And so with regard -to every other agent operating upon the human sensibility: there is, -in each set of circumstances, a sensational equivalent of alcohol, of -odors, of music, of spectacle. - -It is this definite relation between outward agents and the human -feelings that renders it possible to discuss human interests from the -objective side, the only accessible side. We cannot read the feelings -of our fellows; we merely presume that like agents will affect them all -in nearly the same way. It is thus that we measure men’s fortunes and -felicity by the numerical amount of certain agents, as money, and by -the absence or low degree of certain other agents, the causes of pain -and the depressors of vitality. And, although the estimate is somewhat -rough, this is not owing to the indefiniteness of the sensational -equivalent, but to the complications of the human system, and chiefly -to the narrowness of the line that everywhere divides the wholesome -from the unwholesome degrees of all stimulants. - -Let us next represent the equivalence under vital or physiological -action. The chief organ concerned is the brain; of which we know that -it is a system of myriads of connecting threads, ramifying, uniting, -and crossing at innumerable points; that these threads are actuated -or made alive with a current influence called the nerve force; that -this nerve-force is a member of the group of correlating forces; -that it is immediately derived from the changes in the blood, and in -the last resort from oxidation, or combustion, of the materials of -the food, of which combustion it is a definite equivalent. We know, -further, that there can be no feeling, no volition, no intellect, -without a proper supply of blood, containing both oxygen and the -material to be oxidized; that, as the blood is richer in quality in -regard to these constituents, and more abundant in quantity, the mental -processes are more intense, more vivid. We know also that there are -means of increasing the circulation in one organ, and drawing it off -from another, chiefly by calling the one into greater exercise, as -when we exert the muscles or convey food to the stomach; and that, -when mental processes are more than usually intensified, the blood is -proportionally drawn to the brain; the oxidizing process is there in -excess, with corresponding defect and detriment in other organs. In -high mental excitement, digestion is stopped; muscular vigor is abated -except in the one form of giving vent to the feelings, thoughts, and -purposes; the general nutrition languishes; and, if the state were long -continued or oft repeated, the physical powers, strictly so called, -would rapidly deteriorate. We know, on the other extreme, that sleep -is accompanied by reduced circulation in the brain; there is in fact a -reduced circulation generally; while of that reduced amount more goes -to the nutritive functions than to the cerebral. - -In listening to Dr. Frankland’s lecture on “Muscular Power,” delivered -at the Royal Institution of London, I noticed that, in accounting for -the various items of expenditure of the food, he gave “mental work” as -one heading, but declined to make an entry thereinunder. I can imagine -two reasons for this reserve, the statement of which will further -illustrate the general position. In the first place, it might be -supposed that mind is a phenomenon so anomalous, uncertain, so remote -from the chain of material cause and effect, that it is not even to be -mentioned in that connection. - -To which I should say, that mind is indeed, as a phenomenon, widely -different from the physical forces, but, nevertheless, rises and falls -in strict numerical concomitance with these: so that it still enters, -if not directly, at least indirectly, into the circle of the correlated -forces. Or, secondly, the lecturer may have held that, though a -definite amount of the mental manifestations accompanies a definite -amount of oxidation in the special organs of mind, there is no means -of reducing this to a measure, even in an approximate way. To this I -answer, that the thing is difficult but not entirely impracticable. -There is a possibility of giving, approximately at least, the amount of -blood circulating in the brain, in the ordinary waking state; and, as -during a period of intense excitement we know that there is a general -reduction, almost to paralysis, of the collective vital functions, -we could not be far mistaken in saying that, in that case, perhaps -one-half or one-third of all the oxidation of the body was expended in -keeping up the cerebral fires. - -It is a very serious drawback in any department of knowledge, where -there are relations of quantity, to be unable to reduce them to -numerical precision. This is the case with mind in a great degree, -although not with it alone; many physical qualities are in the same -state of unprecise measurement. We cannot reduce to numbers the -statement of a man’s constitutional vigor, so as to say how much he -has lost by fatigue, by disease, by age, or how much he has gained by -a certain healthy regimen. Undoubtedly, however, it is in mind that -the difficulties of attaining the numerical statement are greatest if -not nearly insuperable. When we say that one man is more courageous, -more loving, more irascible than another, we apply a scale of degree, -existing in our own mind, but so vague that we may apply it differently -at different times, while we can hardly communicate it to others -exactly as it stands to ourselves. The consequence is, that a great -margin of allowance must always be made in those statements; we can -never run a close argument, or contend for a nice shade of distinction. -Between the extremes of timidity and courage of character the best -observer could not entertain above seven or eight varieties of -gradation, while two different persons consulting together could hardly -agree upon so minute a subdivision as that. The phrenologists, in their -scale of qualities, had the advantage of an external indication of -size, but they must have felt the uselessness of graduating this beyond -the delicacy of discriminating the subjective side of character; and -their extreme scale included twenty steps or interpolations. - -Making allowance for this inevitable defect, I will endeavor to present -a series of illustrations of the principle of correlation as applied -to mind, in the manner explained. I deal not with mind directly, but -with its material side, with whose activity, measured exactly as we -measure the other physical forces, true mental activity has a definite -correspondence. - -Let us suppose, then, a human being with average physical constitution, -in respect of nutritive vigor, and fairly supplied with food and with -air, or oxygen. The result of the oxidation of the food is a definite -total of force, which may be variously distributed. The demand made -by the brain, to sustain the purely mental functions, may be below -average, or above average; there will be a corresponding, but inverse, -variation of the remainder available for the more strictly physical -processes, as muscular power, digestive power, animal heat, and so on. - -In the first case supposed, the case of a small demand for mental work -and excitement, we look for, and we find, a better _physique_--greater -muscular power and endurance, more vigor of digestion, rendering a -coarser food sufficient for nourishment, more resistance to excesses of -cold and heat; in short, a constitution adapted to physical drudgery -and physical hardship. - -Take, now, the other extreme. Let there be a great demand for mental -work. The oxidation must now be disproportionately expended in the -brain; less is given to the muscles, the stomach, the lungs, the skin, -and secreting organs generally. There is a reduction of the possible -muscular work, and of the ability to subsist on coarser food, and -to endure hardship. Experience confirms this inference; the common -observation of mankind has recognized the fact--although in a vague, -unsteady form--that the head-worker is not equally fitted to be a -hand-worker. The master, mistress, or overseer has each more delicacy -of sense, more management, more resource, than the manual operatives, -but to these belongs the superiority of muscular power and persistence. - -There is nothing incompatible with the principle in allowing the -possibility of combining, under certain favorable conditions, both -physical and mental exertion in considerable amount. In fact, the -principle teaches us exactly how the thing may be done. Improve the -quality and increase the quantity of the food; increase the supply -of oxygen by healthy residence; let the habitual muscular exertion -be such as to strengthen and not impair the functions; abate as much -as possible all excesses and irregularities, bodily and mental; add -the enormous economy of an educated disposal of the forces; and you -will develop a higher being, a _greater aggregate_ of power. You -will then have more to spare for all kinds of expenditure--for the -physico-mental, as well as for the strictly physical. What other -explanation is needed of the military superiority of the officer over -the common soldier? of the general efficiency of the man nourished, but -not enervated, by worldly abundance? - -It may be possible, at some future stage of scientific inquiry, to -compute the comparative amount of oxidation in the brain during severe -mental labor. Even now, from obvious facts, we must pronounce it to be -a very considerable fraction of the entire work done in the system. The -privation of the other interests during mental exertion is so apparent, -so extensive, that if the exertion should happen to be long continued, -a liberal atonement has to be made in order to stave off general -insolvency. Mental excess counts as largely as muscular excess in the -diversion of power; it would be competent to suppose either the one -or the other reducing the remaining forces of the system to one-half -of their proper amount. In both cases, the work of restoration must -be on the same simple plan of redressing the inequality, of allowing -more than the average flow of blood to the impoverished organs, for a -length of time corresponding to the period when their nourishment has -been too small. It is in this consideration that we seem to have the -reasonable, I may say the arithmetical, basis of the constitutional -treatment of chronic disease. We _repay the debt to Nature_ by allowing -the weakened organ to be better nourished and less taxed, according to -the degradation it has undergone by the opposite line of treatment. In -a large class of diseases we have obviously a species of insolvency, -to be dealt with according to the sound method of readjusting the -relations of expenditure and income. And, if such be the true theory, -it seems to follow that medication is only an inferior adjunct. Drugs, -even in their happiest application, can but guide and favor the -restorative process; just as the stirring of a fire may make it burn, -provided there be the needful fuel. - -There is thus a definite, although not numerically-statable relation, -between the total of the physico-mental forces and the total of the -purely physical processes. The grand aggregate of the oxidation of the -system includes both; and, the more the force taken up by one, the -less is left to the other. Such is the statement of the correlation -of mind to the other forces of Nature. We do not deal with pure -mind--mind in the abstract; we have no experience of an entity of that -description. We deal with a compound or two-sided phenomenon--mental -on one side, physical on the other; there is a definite correspondence -in degree, although a difference of nature, between the two sides; and -the physical side is itself in full correlation with the recognized -physical forces of the world. - -II. There remains another application of the doctrine, perhaps equally -interesting to contemplate, and more within my special line of study. -I mean the correlation of the mental forces among themselves (still -viewed in the conjoint arrangement). Just as we assign limits to mind -as a whole, by a reference to the grant of physical expenditure, in -oxidation, etc., for the department, so we must assign limits to the -different phases or modes of mental work--thought, feeling, and so -on--according to the share allotted to each; so that, while the mind as -a whole may be stinted by the demands of the non-mental functions, each -separate manifestation is bounded by the requirements of the others. -This is an inevitable consequence of the general principle, and equally -receives the confirmation of experience. There is the same absence of -numerical precision of estimate; our scale of quantity can have but few -divisions between the highest and the lowest degrees, and these not -well fixed. - -What is required for this application of the principle is, to ascertain -the comparative cost, in the physical point of view, of the different -functions of the mind. - -The great divisions of the mind are--feeling, will, and thought; -feeling, seen in our pleasures and pains; will, in our labors to -attain the one and avoid the other; thought, in our sensations, ideas, -recollections, reasonings, imaginings, and so on. Now, the forces of -the mind, with their physical supports, may be evenly or unevenly -distributed over the three functions. They may go by preference either -to feeling, to action, or to thinking; and, if more is given to one, -less must remain to the others, the entire quantity being limited. - -First, as to the feelings. Every throb of pleasure costs something to -the physical system; and two throbs cost twice as much as one. If we -cannot fix a precise equivalent, it is not because the relation is not -definite, but from the difficulties of reducing degrees of pleasure to -a recognized standard. Of this, however, there can be no reasonable -doubt--namely, that a large amount of pleasure supposes a corresponding -large expenditure of blood and nerve-tissue, to the stinting, perhaps, -of the active energies and the intellectual processes. It is a matter -of practical moment to ascertain what pleasures cost least, for there -are thrifty and unthrifty modes of spending our brain and heart’s -blood. Experience probably justifies us in saying that the narcotic -stimulants are, in general, a more extravagant expenditure than the -stimulation of food, society, and fine art. One of the safest of -delights, if not very acute, is the delight of abounding physical -vigor; for, from the very supposition, the supply to the brain is not -such as to interfere with the general interests of the system. But the -theory of pleasure is incomplete without the theory of pain. - -As a rule, pain is a more costly experience than pleasure, although -sometimes economical as a check to the spendthrift pleasures. Pain is -physically accompanied by an excess of blood in the brain, from at -least two causes--extreme intensity of nervous action, and conflicting -currents, both being sources of waste. The sleeplessness of the pained -condition means that the circulation is never allowed to subside from -the brain; the irritation maintains energetic currents, which bring the -blood copiously to the parts affected. - -There is a possibility of excitement, of considerable amount, without -either pleasure or pain; the cost here is simply as the excitement: -mere surprises may be of this nature. Such excitement has no value, -except intellectually; it may detain the thoughts, and impress the -memory, but it is not a final end of our being, as pleasure is; and it -does not waste power to the extent that pain does. The ideally best -condition is a moderate surplus of pleasure--a gentle glow, not rising -into brilliancy or intensity, except at considerable intervals (say a -small portion of every day), falling down frequently to indifference, -but seldom sinking into pain. - -Attendant on strong feeling, especially in constitutions young or -robust, there is usually a great amount of mere bodily vehemence, as -gesticulation, play of countenance, of voice, and so on. This counts as -muscular work, and is an addition to the brain-work. Properly speaking, -the cerebral currents discharge themselves in movements, and are -modified according to the scope given to those movements. Resistance -to the movements is liable to increase the conscious activity of the -brain, although a continuing resistance may suppress the entire wave. - -Next as to the will, or our voluntary labors and pursuits for the great -ends of obtaining pleasure and warding off pain. This part of our -system is a compound experience of feeling and movement; the properly -mental fact being included under feeling--that is, pleasure and pain, -present or imagined. When our voluntary endeavors are successful, -a distinct throb of pleasure is the result, which counts among our -valuable enjoyments: when they fail, a painful and depressing state -ensues. The more complicated operations of the will, as in adjusting -many opposite interests, bring in the element of conflict, which is -always painful and wasting. Two strong stimulants pointing opposite -ways, as when a miser has to pay a high fee to the surgeon that saves -his eyesight, occasion a fierce struggle and severe draft upon the -physical supports of the feelings. - -Although the processes of feeling all involve a manifest, and it may -be a serious, expenditure of physical power, which of course is lost -to the purely physical functions; and although the extreme degrees of -pleasure, of pain, or of neutral excitement, must be adverse to the -general vigor; yet the presumption is, that we can afford a certain -moderate share of all these without too great inroads on the other -interests. It is the thinking or intellectual part of us that involves -the heaviest item of expenditure in the physico-mental department. Any -thing like a great or general cultivation of the powers of thought, or -any occupation that severely and continuously brings them into play, -will induce such a preponderance of cerebral activity, in oxidation and -in nerve-currents, as to disturb the balance of life, and to require -special arrangements for redeeming that disturbance. This is fully -verified by all we know of the tendency of intellectual application to -exhaust the physical powers, and to bring on early decay. - -A careful analysis of the operations of the intellect enables us -to distinguish the kind of exercises that involve the greatest -expenditure, from the extent and the intensity of the cerebral -occupation. I can but make a rapid selection of leading points: - -First. The mere exercise of the senses, in the way of attention, -with a view to watch, to discriminate, to identify, belongs to the -intellectual function, and exhausts the powers according as it is long -continued, and according to the delicacy of the operation; the meaning -of delicacy being that an exaggerated activity of the organ is needed -to make the required discernment. To be all day on the _qui vive_ for -some very slight and barely perceptible indications to the eye or the -ear, as in catching an indistinct speaker, is an exhausting labor of -attention. - -Secondly. The work of acquisition is necessarily a process of great -nervous expenditure. Unintentional imitation costs least, because there -is no forcing of reluctant attention. But a course of extensive and -various acquisitions cannot be maintained without a large supply of -blood to cement all the multifarious connections of the nerve-fibres, -constituting the physical side of acquisition. An abated support of -other mental functions, as well as of the purely physical functions, -must accompany a life devoted to mental improvement, whether arts, -languages, sciences, moral restraints, or other culture. - -Of special acquisitions, languages are the most apparently voluminous; -but the memory for visible or pictorial aspects, if very high, as in -the painter and the picturesque poet, makes a prodigious demand upon -the plastic combinations of the brain. - -The acquisition of science is severe, rather than multifarious; it -glories in comprehending much in little, but that little is made up of -painful abstract elements, every one of which, in the last resort, must -have at its beck a host of explanatory particulars: so that, after all, -the burden lies in the multitude. If science is easy to a select number -of minds, it is because there is a large spontaneous determination of -force to the cerebral elements that support it; which force is supplied -by the limited common fund, and leaves so much the less for other uses. - -If we advert to the moral acquisitions and habits in a well-regulated -mind, we must admit the need of a large expenditure to build up the -fabric. The carefully-poised estimate of good and evil for self, the -ever-present sense of the interests of others, and the ready obedience -to all the special ordinances that make up the morality of the time, -however truly expressed in terms of high and abstract spirituality, -have their counterpart in the physical organism; they have used up -a large and definite amount of nutriment, and, had they been less -developed, there would have been a gain of power to some other -department, mental or physical. - -Refraining from further detail on this head, I close the illustration -by a brief reference to one other aspect of mental expenditure, namely, -the department of intellectual production, execution, or creativeness, -to which in the end our acquired powers are ministerial. Of course, -the greater the mere continuance or amount of intellectual labor in -business, speculation, fine art, or any thing else, the greater the -demand on the _physique_. But amount is not all. There are notorious -differences of severity or laboriousness, which, when closely examined, -are summed up in one comprehensive statement--namely, the number, -the variety, and the conflicting nature of the conditions that have -to be fulfilled. By this we explain the difficulty of work, the toil -of invention, the harassment of adaptation, the worry of leadership, -the responsibility of high office, the severity of a lofty ideal, -the distraction of numerous sympathies, the meritoriousness of sound -judgment, the arduousness of any great virtue. The physical facts -underlying the mental fact are a wide-spread agitation of the cerebral -currents, a tumultuous conflict, a consumption of energy. - -It is this compliance with numerous and opposing conditions that -obtains the most scanty justice in our appreciation of character. -The unknown amount of painful suppression that a cautious thinker, -a careful writer, or an artist of fine taste, has gone through, -represents a great physico-mental expenditure. The regard to evidence -is a heavy drag on the wings of speculative daring. The greater the -number of interests that a political schemer can throw overboard, the -easier his work of construction. The absence of restraints--of severe -conditions--in fine art, allows a flush and ebullience, an opulence of -production, that is often called the highest genius. The Shakespearean -profusion of images would have been reduced to one-half, if not less, -by the self-imposed restraints of Pope, Gray, or Tennyson. So, reckless -assertion is fuel to eloquence. A man of ordinary fairness of mind -would be no match for the wit and epigram of Swift. - -And again. The incompatibility of diverse attributes, even in minds of -the largest compass (which supposes equally large physical resources), -belongs to the same fundamental law. A great mind may be great in many -things, because the same kind of power may have numerous applications. -The scientific mind of a high order is also the practical mind; it is -the essence of reason in every mode of its manifestation--the true -philosopher in conduct as well as in knowledge. On such a mind also, -a certain amount of artistic culture may be superinduced; its powers -of acquisition may be extended so far. But the spontaneous, exuberant, -imaginative flow, the artistic nature at the core, never was, cannot -be, included in the same individual. Aristotle could not be also a -tragic poet; nor Newton a third-rate portrait-painter. The cost of one -of the two modes of intellectual greatness is all that can be borne by -the most largely-endowed personality; any appearances to the contrary -are hollow and delusive. - -Other instances could be given. Great activity and great sensibility -are extreme phases, each using a large amount of power, and therefore -scarcely to be coupled in the same system. The active, energetic man, -loving activity for its own sake, moving in every direction, wants the -delicate circumspection of another man who does not love activity for -its own sake, but is energetic only at the spur of his special ends. - -And once more. Great intellect as a whole is not readily united with a -large emotional nature. The incompatibility is best seen by inquiring -whether men of overflowing sociability are deep and original thinkers, -great discoverers, accurate inquirers, great organizers in affairs; or -whether their greatness is not limited to the spheres where feeling -performs a part--poetry, eloquence, and social ascendency. - - -THE END. - - -FOOTNOTES: - -[18] For the fuller elaboration of the point here referred to, see -Chapter VII., Professor Bain’s “Mind and Body”--an earlier volume in -the present series. - - - - -INDEX. - - - Absorbed heat changed into chemical separation, 114. - into actual visible energy, 105. - into light and heat, 117. - - Acquisition, 232. - - Actinic rays, 129. - - Action and reaction equal and opposite, 8. - - Affinity, chemical, 53. - - Air and water in motion, 147. - - Albuminoids, 177, 183. - - Amber, 61. - - Ampère, 75. - - Amyloids, 177, 183. - - Ancients, their ideas not prolific, 135. - - Andrews, 141. - - Animal heat, 207. - - Animals, how they live, 188. - - Animals and inanimate machines, 165. - - Aristotle on a medium, 134. - on mind and body, 207. - - Atmospheric circulation, 109. - - Atomic forces and heat, 58. - - Atomic or chemical separation, 80. - - Atoms and molecules, 51. - - Attention, 232. - - Attraction, molecular, 52. - mutual, of atoms, 54. - and repulsion of magnets, 75. - of electric currents, 75. - - - Bacon, 133, 137. - - Battery of Grove, 70. - - Budding, 180. - - - Caloric, 38. - - Carnivora, 189. - - Chemical affinity, 53. - and electrical attraction, 64. - and heat, 58. - - Chemical combination producing heat, 119. - - Chemical instability, 156. - - Chemical separation converted into electrical separation, 122. - into electricity in motion, 123. - - Chlorophyll, 177. - - Chrysalis, 187. - - Circulation of the atmosphere, 109. - - Clausius, 141. - - Cohesion, force of, 51. - - Cold apparently produced by the electric current, 126. - - Conduction of electricity, 61. - - Conservation, laws of, 82. - theory of, 140. - - Crossbow and watch-spring, 25. - - Current, the electric, 69. - and magnetism, 72. - heating effect of, 73. - chemical effect of, 74. - - Currents, electric, attraction and repulsion of, 74. - induction of, 75. - - - Dalton, 133. - - Davy, Sir Humphrey, 38, 137. - - Democritus on atoms, 133. - - Descartes, 136. - - Diastase, 184. - - Disease-germs, 3. - - Dissipation of energy, 141. - - Dissociation, 115. - - - Egg, development of the, 186. - - Electric current, 69. - and magnetism, 72. - heating effect of, 73. - chemical effect of, 74. - induction, 65. - - Electrical attraction and chemical affinity, 64. - - Electrical separation, 81. - when produced, 64. - transmuted into visible motion, 124. - into electric current, 124. - - Electro-magnetism, 72. - - Elastic forces, 50. - - Electricity, 60. - vitreous and resinous, 63. - negative and positive, 63. - theory of, 63. - in motion, 81. - transmuted into visible motion, 124. - into heat, 125. - into chemical separation, 127. - - Encke’s comet, 96. - - Energies, list of, 78-82. - natural, and their sources, 143. - - Energy, meaning of, 1-22. - of bodies in motion proportional to their weight or mass, 14. - proportional to the square of the velocity, 19. - of visible motion, its transmutation, 87. - visible, transformed into absorbed heat, 88. - dissipation of, 141. - transmutations of, 27. - varies as the square of the velocity, 15. - of motion, 24. - transformed into electrical separation, 98. - of position, a sort of capital, 26. - - Equilibrium, 154. - - Etiolation, 180. - - - Fermentation, 183. - - Food, 145. - - Force, vital, whence derived, 171. - physical, 194. - chemical, 194. - of chemical affinity, 53. - of cohesion, 51. - - Force, mechanical or molar, 205. - molecular, 205. - - Friction, 35. - - - Heat, absorbed, changed into chemical separation, 114. - into electrical separation, 115. - into electricity in motion, 116. - - Heat-units of different substances, 119. - - Heat-motion, 80. - - Heat-engines, their essential conditions, 107. - - Helmholtz, 141. - - Heraclitus on energy, 133. - - Herbivora, 191. - - Heterogeneity essential in electrical development, 64. - - Huyghens, 137. - - Hydraulic press, 32. - - - Inclined plane, 28. - - Incubation, 186. - - Individuals, our ignorance of, 1. - - Induction, electric, 65. - of electric currents, 75. - - Instability, mechanical, 155. - chemical, 156. - - Intellectual labor, 234. - - - Joule, 137, 140, 141. - - Joule’s experiments on work and heat, 44. - - - Kilogrammetre, 16. - - - Larva, 187. - - Latent heat, 57. - - Laws of conservation, 82. - - Life depends on the sun, 165. - - Light, a perpetual, impossible, 149. - - Lime, carbonate, easily decomposed, 58. - - List of energies, 78-82. - - - Machines, their true function, 33. - animated and inanimate, 157. - - Magnets, attachment and repulsion of, 75. - - Maxwell, 141. - - Mayor, 140. - - Mechanical energy changed into heat, 23. - equivalent of heat, 43. - force, 205. - instability, 155. - - Mental forces, mutual correlations of, 227-236. - - Mind, its correlations to natural forces, 218-227. - and body, 207, 211. - - Molar force, 205. - - Molecular attraction and heat, 55. - separation, 80. - - Molecules, ultimate, of matter, 5. - their motions, 7. - and atoms, 51. - - Motion changed into an electric current, 99. - - Muscular power, 207. - - - Narcotic stimulants, 229. - - Negative and positive electricity, 63. - - Nerve power, 207. - - Newton, 136, 137. - - Non-conductors of electricity, 61. - - - Percussion, 36. - - Perpetual motion, 139. - - Physical force, 194. - - Plants growing at night, 181. - - Positive and negative electricity, 63. - - Protoplasm, 177. - - Pulleys, their function, 30. - - - Radiant energy, 81. - converted into absorbed heat, 123. - promoting chemical separation, 123. - - Rankine, 141. - - Resinous and vitreous electricity, 63. - - Rotation of earth retarded, 95. - - Rumford, 39, 137. - - - Silver oxide readily decomposed, 58. - - Solar rays, decomposition by, 59. - - Sulphur, 146. - - Sun--a source of high-temperature heat, 148. - - Sun’s heat, origin of, 150. - spots, auroras, and cyclones correlated, 98. - - - Tait, 141. - - Temperature of dissociation, 115. - - Thermo-electricity, 116. - - Thermopile, 117. - - Thomas Aquinas, 209. - - Thomson, William and James, 140. - - Tides, 146. - - Tissues, decay of, 164. - - - Universe, its probable fate, 152. - - Units of heat and work, 46. - - - Vegetation, 176. - - Velocity and energy, relation between, 16. - - Virtual velocities, 34. - principle of, its history, 137. - - Vital force, whence derived, 171. - - Vitality, 194. - - Vitreous and resinous electricity, 63. - - Voltaic current, 69. - and magnetism, 72. - heating effect of, 73. - chemical effect of, 74. - - - Water at high level, 24. - - Watt, 138. - - Wild’s electro-magnetic machine, 103. - - Will, 194. - - Work, definition of, 15. - unit of, 15. - rise of true conceptions regarding, 138. - - - Yeast-plant, 185. - - -THE END. - - - - -Transcriber’s Notes - -Errors in punctuation have been fixed. - -Page 60: “heterogenous bodies” changed to “heterogeneous bodies” - 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