BOUGHT WITH THE INCOME FROM THE SAGE ENDOWMENT FUND THE GIFT OF fli»nrg W. Sage 1891 J.o\^ q4 a,o|-:»[(^{>fa 5901 .„„„_ Cornell University Library arV18694 Molecular forces and Newtonian laws .. 3 1924 031 289 303 oiin.anx The original of tliis bool< is in tine Cornell University Library. There are no known copyright restrictions in the United States on the use of the text. http://www.archive.org/details/cu31924031289303 MOLECULAR FORCES AND NEWTONIAN LAWS. By ALEX. CLARK, M.A. ALL RIGHTS RESERVED. ©lasgow: W. & R. HOLMES, DuNLOP Street. 1905. CORRECTIONS AND ADDITIONS. Page '21, line 25. — For "amounted," read " amount." Page 57, line 21. — Add "The couples are equal when the bar subtends equal angles at N and S ; for, by the nature of radiation, the polar forces are then equal, and their resultant, which bisects the angle between them, is a constant quantity, if the sum of the polar distances is constant, which is the ease at every point in the circumference of an ellipse." Page 59, line 6. — For " ratio of the two component forces," read " direction of the resultant force." Page 61, line 5. — Delete remainder of paragraph after the semi- colon, and insert, "for, either energy would be increased or diminished by the amount of repulsion, or the constitution of matter would be changed." Page 88, last line. — The reason of the law here stated for the radiation of electric force, which is the same as that of magnetism, is given in the proposed addition at page 57, and Note 20 may be cancelled. Page 124, line 32.— For " time '' read " times." Page 129, line 31. — The term inclination is commonly used synonymously with dip. In this work it always denotes the angle which a magnetic substance makes with the direction of its motion through the magnetising rays, or of the rays through the substance. Page 184, line 13. — For " poles," read "pole." Page 216, line 30. — For " attraction," read " attractive." Page 222, line 6.— For " art," read " act." PREFACE. npHE views given of the Molecular Forces in this work have been obtained by deduction from the Newtonian Laws, and differ materially from the current theories on the subject. The author believes that the general principles of Magnetism, Electricity, and Chemical Affinity have been established beyond reasonable doubt ; but, in a field so wide, and much of it comparatively new, he cannot hope to have altogether escaped error in some of the details. If any such errors occur to the Reader, he will confer a favour upon the author by calling his attention to them. CONTENTS. PAGE iNTBOnnCTION, 9 CHAPTER I. FORCE AND ENERGY. 1. Universal Attraction, 13 ■2. Distinction between Force and Energy, 15 3. Different Forms of Force and Energy, 16 4. Kinetic and Potential Energy, 18 5. Heat, 20 6. Transmission of Energy, 22 7. Polarity and Elasticity of Matter, 24 8. Interchanges of Kinetic and Potential Energy, 27 9. Mechanical Power, 31 10. Lines of Force, 34 11. One Law for all Masses and Distances, 39 CHAPTER II. MAGNETISM. 1. Magnetics and Non-Magnetics, 41 2. Magnetism, a Form of Gravitation, 43 3. Polarisation of Magnetics, 45 4. Magnetism and Gravitation, 48 ."). Magnetic Circuit, 51 6. Magnetic "Induction," 53 7. Conveotive and Directive Force, 58 8. No Magnetic Repulsion, 60 6 Contents. CHAPTER III. ELECTRICITY. 1. Electricity, a Force of Attraction, 71 2. Electricity and Magnetism, 74 3. Electricity and Work, 77 4. How Electricity is Generated, . 80 5. Different Ways of Generating Electricity, H3 6. Conductors and Non-Conductors, 85 7. Electric Force through a Non-Conductor, 87 8. Electrical "Induction," 91 9. No Electrical Repulsion, 94 CHAPTER IV. ELECTRICAL PHENOMENA. 1. Electricity at the Surface only, 99 2. Electrical Condensation, 102 3. The Cascade, 104 4. The Lightning Conductor, 106 5. Multiplex Telegraphy, 108 6. Wheatstone's Bridge, 110 7. Electrical Potential, 112 8. The Electrical Engine, 116 CHAPTER V. ELECTRO-MAGNETISM AND DIAMAGNETISM. 1. Different Modes of Magnetisation, 119 2. The Hertzian Waves, 121 3. Electro-Magnetisation, 125 4. The Three Magnetic Elements, 128 5. Magnetisation of Atmospheric Air, 133 6. Electro-Dynamics, 138 7. Diamagnetism, 14q Contents. 7 CHAPTER VI. TERRESTRIAL MAGNETISM. 1. Defective Theories, 145 2. The Atmosphere Magnetised by Solar Heat, 148 3. Direction of Magnetisation, 150 4. Relation of Needle to Magnetic Poles, 155 T). Declination and Inclination, , 158 6. Movement of Magnetic Pole. 161 7. Variation of Declination, 165 8. Variation of Dip, 170 9. Magnetic Intensity, 176 10. Magnetic Irregularities, 179 CHAPTER VII. ATMOSPHERIC ELECTRICITY. 1. The Atmosphere, an Electrical Machine, 186 2. Electrical Direction, 188 .3. Earth Currents, 190 4. Magnetic Storms, 192 CHAPTER VIII. IDENTITY OF THE FORCES. 1. Matter and its Properties, 195 \2. Gravitation, 197 3. Cohesion, 199 i. Chemical Affinity, 201 5\ Magnetism, 204 el Electricity, 206 7. How Force Operates, 209 Explanatory Notes, 215 INTRODUCTION. rpHE triumph of modern science is nowhere more •*- striking than in the department of electricity and magnetism. Not only are all the principal places on the earth's surface connected by telegraphic cables, but com- munication is also established through the atmosphere between distant lands and between ships in mid ocean. Merchants transact their business sitting each at his own desk, and their merchandise is directed unerringly day and night over the seas by an element so subtle that it eludes our senses. And yet our knowledge of electricity and magnetism, from a scientific point of view, is most dis- appointing. In the opening pages of nearly every treatise on the subject, we are confronted with the confession, " We do not know what electricity and magnetism are;" and instead of knowledge we have to be satisfied with a series of hypotheses, some of them less unreliable than others, but all of them, at best, only guesses at the truth. Certain phenomena have been observed, and advantage taken of them for practical purposes, but we do not reason scientifically on the subject. In short, our knowledge of electricity, magnetism, and cognate forces, is still in the empirical stage. The mathematicians have not added materially to our knowledge. The function of mathematics is to determine quantitative relations in accordance with known laws ; not to discover laws that are unknown. Clerk Maxwell's Treatise on Electricity and Magnetism, was little more 10 Molecular Forces and Newtonian Laws. than a translation into mathematical symbols of the results obtained experimentally by Faraday. It contained nothing new. Maxwell could have explained his own formulae only by re-translating them into the language of the great experimentalist. Since the appearance of Maxwell's great work, it has been customary in treatises on electricity and magnetism to make a liberal use of higher mathematics. The need of that instrument, however, diminishes as our knowledge increases ; because, the laws being simplified, the relations are more easily expressed. In this work use is made of elementary mathematics only, which has the advantage of bringing the results within reach of the ordinary reader, or the intelligent workman, who has only a limited acquaintance with mathematical science. Whatever the precise nature of electricity and mag- netism, it is certain that they are forms of force, for they originate motion. But the general laws of force and motion were clearly stated by Newton ; and as these laws have stood the test of 200 years, it may be accepted as a condition of arriving at a correct knowledge of electric and magnetic force, that the Newtonian laws be adhered to. It is no valid objection to this condition that the forces are molecular, for matter is regulated by the same laws, whether in large or small masses, and irrespective of distance. The relative force and motion of two molecules of vapour in the air are the same as of two planets in the solar system. Where difficulties present themselves in connection with these molecular forces, it has been the mistake of observers to formulate theories to account for the phenomena, instead of seeking to reconcile them with general laws. In certain circumstances, for instance, bodies move away from each other, and this has been hastil}' ascribed to repulsion, whereas careful consideration Introduction. 11 would have shown that such motion is due to attraction, just as the ascending of smoke, no less than the falling of a stone, is a proof of universal gravitation. In this work the Newtonian laws have been strictly adhered to, and any theories at variance with these laws set aside, by whatever authority supported. Against these laws no individual opinions should have any weight. And this view is fully borne out by the results. After a little consideration all difficulties vanish, and it is shown that not only electricity and magnetism, but also gravitation, cohesion, and chemical aflfinity, are in strict conformity with the Newtonian laws of force and motion. Most of the points about which difficulty may be felt, have been apprehended more or less clearly by previous writers, and some of these are referred to in the Explan- atory Notes at the end of the volume. But no one has hitherto reduced all the phenomena to general laws, and thereby put our knowledge of the molecular forces on a scientific basis. This has been attempted in the present work. The first chapter contains a brief outline of general physics, which will probably be found sufficient to enable such readers as have not been instructed in that subject, to follow without difficulty the reasoning upon which the conclusions are based. CHAPTER I. FORCE AND ENERGY. 1. Universal Attraction. rPHE Newtonian law runs thus : — " Every particle of J- matter in the universe attracts every other particle with a force, whose direction is that of the line joining the two, and whose magnitude is directly as the product of their masses, and inversely as the square of their distance from each other." Let A and B be two bodies, the former containing m,, and the latter m', par- ticles. Since there is attraction between every particle of the one and every particle of the other, the total force between them is m mf. If d be the distance between A and B, and / the force of attraction at that distance, by the above aw / = -^■ The terms force and weight are synonymous. If A represents the earth, and B the small piece of platinum Kept in the Exchequer Office, London, as the standard weight for commercial purposes, and d the distance from B 14 Molecular Farces and JVetvtonian Laws. the centre of the earth to sea-level at London, then /= 1 pound, or the standard unit of force or weight for this country. The only measure of the mass, or quantity of matter contained in any body, is the force of attraction between it and some other body of constant quantity. In all countries the standard mass of reference is the earth. Force has no relation to time. Of the three quantities, mass, distance, and force, if any two be given the third can be found. Time does not enter into the calculation. Force is therefore a relation between particles of matter which varies according to distance only. This applies to the variation of attraction due to temperature, which can affect the force of attraction between particles only by affecting the distance between them. The terms particle, atom, and molecule, are of such constant occurrence in treating of matter and force, that it may be well to define them. A particle is any small quantity of matter. The term is purely relative. A grain of sand is a particle with reference to the earth : the earth is itself a particle with reference to the system of suns and plants, of which it forms a very small part. An atom, is the smallest known sub-division of any elementary- substance. Such atoms are of very different weights or masses. An atom of oxygen is about 16 times, and an atom of iron about 56 times, the weight of an atom of hydrogen. These are called atomic weights. The force of attraction between such substances depends, of course, upon their weight and not the number of the atoms. A molecule is the smallest sub-division of a substance com- posed of two or more elements. Thus, a molecule of water consists of two atoms of hydrogen and one of oxygen. Its weight, or mass, is therefore equal to about 18 atoms of hydrogen. Force and Energy. 15 2. Distinction between Force and Energy. By Newton's first law of motion, " Every body continues . in its state of rest or of uniform motion in a straight line, except in so far as it may be compelled by impressed force to change that state." The property of matter defined by this law is called inertia. According to the law of gravitation, wherever matter exists there is a force of attraction between its particles. The converse proposition is also true, at least in pure physics, that wherever force exists there is matter to whose attraction it is due. It may, therefore, be inferred that force is a property of matter. Newton's law rather implies that force is impressed iipon matter from without, but the law of motion is the same if we suppose force to be inherent in matter, which is probably the case. Since particles of matter attract one another according to the law of inverse squares, absolute rest would only be possible if all the matter in the universe were uniformly distributed over unlimited space, for then only would every particle be attracted equally in all directions. Two or more particles may be relatively at rest, but absolute rest is impossible in the present state of the universe, at least in that part of it to which we belong. Every particle of matter is necessarily in a state of motion, and the term energy is used to denote matter in motion. Force is a property of matter ; motion is only an accident. Energy is produced by force acting upon matter through distance, and the mechanical value of the energy is the product of the force into the distance through which it acts. This is commonly called work, and the ordinary unit of work in this country is the foot-pound, or a force of one pound weight acting through a distance of one foot. 16 Molecular Forces and Newtonian Laws. Energy is measured by the number of foot-pounds which it can perform in a second, or unit, of time. The distance through which a body moves in a second is called its velocity; and since the body can have no energy except what is imparted to it by the action of force, it is obvious that the energy of a moving body can be expressed in terms of its mass and velocity. Thus, the energy of a body having a mass m and velocity v, is equal to ™^ foot-pounds of work, where g is the velocity acquired by a falling body in one second, or 32'2 feet, very nearly. 3. Different Forms of Force and Energy. The only force of which we possess any certain know- ledge is attraction, which draws all particles of matter towards one another. That force, however, presents itself to us in various forms, and is designated by different names. The principal of these are gravitation, cohesion, chemical affinity, magnetism, and electricity. In the course of this work it will be shown that all these are only so many modifications of the forc6 of attraction inherent in matter, and the nature of these modifications will, as far as possible, be explained. (See Note 1). In works on electricity and magnetism a very prominent place is assigned to repulsion. But the impression that there is such a force appears to arise from a mis- interpretation of facts ; for it is in direct opposition to the Newtonian law of universal gravitation. If it be said that in certain circumstances particles of matter may have repulsion as well as attraction, the force of attraction must always be the greater of the two ; for otherwise they would Ibrm an exception to the law of gravitation. But Force and Energy. 17 to suppose that particles have both 'attraction and repul- sion, the former being ahvays the greater, amounts to nothing. Suppose A and B to be two bodies having between them a force of attraction a, and a force of repulsion h, the resultant of these forces is a net attraction a - &, which may be called c. And c is a constant quantity ; for if the ratio of a to 6 varied, there would be an exception to the law of inverse squares. It will be shown hereafter that all the facts of electricity, magnetism, and diamag- netism, can be accounted for without repulsion. The assumption of such a force appears to be one of the chief reasons why the nature of electricity and magnetism has never been correctly apprehended. In this work the Newtonian laws of force and motion will be strictly adhered to. (See Note 2.) Energy also presents itself to us in various forms. The principal of these are, (1), the motion of the ether, and (2), the motion of solid niatter. Motion of the ether is commonly called radiant heat ; but, more correctly, it is that motion of the ether which causes the sensation of heat. Cold and heat are animal sensations — matter knows only rest and motion. The motion of solid matter is either molecular or mechanical. Molecular einergy is a mode of motion among the particles of a body, whereby they form alternate contacts and separations, so that the motion is of a vibratory nature. Energy is called mechanical when a whole body moves, that is, when all its particles move in the same direction. Such motion can be used for mechanical purposes, whereas the molecular motions are too subtle for manipulation. All these forms of energy are regulated by the same laws. Molecular energy is only micro-mechanical energy. The forces and distances are small, but the vibrations are B 18 Molecular Forces and Newtonian Laws. inconceivably rapid. Thus a body at a high temperature contains a large amount of energy, although the movement is imperceptible. The same law applies to the motion of the ether, which is known to be of a vibrational, or wave, form. The energy which it possesses is measured by the product of the force into the distance through which it acts, the same as that of a falling body or the motion of a planet. These are the conclusions to which we are led by the Newtonian laws of force and motion, and their correctness will become more apparent as we proceed. 4. Kinetic and Potential Energy. We have defined energy as matter in motion, but the term is used in a more general sense. Energy is produced by force acting upon matter through distance, and when there is force between two bodies, with a distance between them through which the force can act, it is common to speak of the product of the force into the distance as potential, or possible, energy; because the force is capable of producing so much energy when action takes place. Let M be a body, whose weight is / and whose mass is m, falling through the distance d, from A to B. When the body is at A, it has no energy, but it can fall through the distance d, and is therefore said to have a potential energy / d. When the body falls to B, it has acquired a ve- locity V, and has therefore |B an energy oi -^ — ihis is called actual or kinetic energy. The sum of all the potential and kinetic energy in the universe is an invariable quantity. Force and Energy. 19 Force can never be expended, because it is a property of matter and is present wherever matter is. But the distance through which the force can act may be exhausted so that it can produce no more energy. Thus, while force can never be expended, potential energy can be expended; and potential energy is never expended without producing an equivalent amount of kinetic energy. In like manner, kinetic energy is never expended without producing an equivalent amount of potential energy. The one form of energy may be converted into the other, but their sum is always the same. If, for instance, the body, M, be taken midway between A and B, as represented in the figure, it has both kinetic and potential energy, but their sum is equal to the whole potential energy at A, or the whole kinetic energy at B. This principle is called the conser- vation of energy, and implies that energy, like matter, can neither be created nor destroyed. In the case above supposed this principle is expressed by the equation f d = *" , the first side of the equation denoting the energy 2(/ of the body at A, the second its energy at B. (See Note 3.) In Newton's time the conservation of energy was not understood. The work expended in moving a body was supposed to be entirely lost. But his third law of motion, that " action and reaction are equal and opposite," ex- presses the same principle in different terms. The action and reaction of Newton are synonymous with kinetic and potential energy as presently in use; and it affords the strongest testimony to the accuracy of his observation of nature.that he was able to express in that third law of motion the operation of a principle that was not yet understood. Just before the body, M, touches the ground at B, its energy is mechanical, but as soon as it touches the ground 20 Molecular Forces avd Newtonian Laws. the mechanical is converted into molecular energy. The nature of that change is easily explained. The particles of the solid body are held together by the force of cohesion, which is simply the force of attraction between the particles, the distance through which it can act being exhausted. That force is then at its maximum, according to the law of inverse squares. By the nature of inertia all the particles of the body tend to move in the same direction and with the same velocity as they have acquired just before the body touches the ground. When concus- sion takes place a strain is put upon the forces of cohesion, and the particles are slightly separated from one another. That action takes place against the forces of cohesion, and all the particles are thereby put into a state of potential energy, the same as when a heavy body is raised from the ground ; and the sum of the products of all these molecular forces into the distances through which they can act is equal to fd, the potential energy of the body at A. The kinetic energy of the body acquired by its fall is thus converted once more into potential energy, but of a molecular instead of a mechanical form. In a scholium to his third law of motion, Newton instances weight or gravitation, friction, and cohesion or viscosity as forms ' of resistance to the motion of a body. But, in overcoming these resistances, work is done against the force of attraction, either in a mechanical or molecular form, so that Newton's term " reaction " is the exact equivalent of what is now meant by potential energy. 5. Heat. When a body in motion impinges upon another solid body, its particles are put into a state of potential energy by the concussion. If the body is brittle, and the shock Force and Energy. 21 sufficiently powerful, it goes to pieces, and its kinetic energy is dissipated in forms partly mechanical and partly molecular. But if the force of cohesion among the particles of the body is sufficiently strong to withstand the shock, that force immediately brings the particles once more into contact, and the running down of the potential energy produces once more an equivalent amount of kinetic energy. A vibratory motion is thus set up among the particles of the body, and to that vibratory motion the term heat is applied. This vibratory motion, once begun, would be perpetual, unless the energy were communicated to some other body, which takes place by conduction and radiation. While that dissipation of the energy is going on, the vibration continues, just as the vibration of a pendulum continues for a time after it has been set in motion, or the waves of the ocean continue to roll for a time after the storm is past. (See Note 4.) The amount of heat in a solid body, or its mechanical value, depends upon the mass of matter in motion, and upon the length and rapidity of the vibrations. There does not appear to be, as yet, any means of measuring the length of these small movements, but their number can be ascertained approximately by the corresponding vibrations which they produce in the ether. In an ordinary white heat they amounted to many millions of millions per second. At every one of these vibrations there is an interchange of kinetic and potential energy, the action of the former always causing separation of the particles, and the action of the latter always causing contact. It thus appears that attraction and energy are the direct opposites of each other, the former always drawing the particles of matter towards each other, and the latter always causing motion in the opposite direction. To this action and 22 Molecular Forces and Neivtonian Laws. reaction, not heat only, but all the phenomena of nature may be reduced. Particles of matter are brought together by their attraction and separated by their energy ; there is no other known cause of motion. From the nature of heat it is obvious that it can never become latent, but the energy may either assume another form, or be converted into potential energy. It is common to speak of the latent heat of steam, because a certain amount of heat must be expended to convert boiling water into steam at the same temperature. But the heat does not become latent. If the steam is retained in the boiler, it occupies, at the same temperature, a space about 1,700 times the volume of the water, and its potential energy is therefore much greater, for the particles have more distance through which they can move under the force of attraction. The energy is also to be found partly in the form of motion among the particles, in accordance with the kinetic theory of gases. Thus, the heat expended in converting the water into steam is not latent, but converted partly into potential energy and partly into kinetic energy in another form. (See Note 5.) 6. Transmission of Energy. The energy possessed by any body may be transmitted to any other body, but it is necessary that the two bodies should be in contact with each other ; for otherwise a body would produce energy where it is not, which is impossible. The idea of one body acting upon another at a distance has been abandoned as unscientific. When it is said that energy is transmitted from one body to another through an intervening medium, the only meaning is that the energy is transmitted from the moving body to the medium, and then from the medium to the other body. Force and Energy. 23 When one billiard ball strikes another and comes to rest, the energy of the first ball is transmitted to the second. In this case the energy of the second ball is practically the same as that of the first, because the elasticity of ivory balls, within certain limits, is nearly perfect, which means that no part of the mechanical energy is converted into molecular energy by the impact. With most substances a large proportion of the energy is so converted, and the mechanical energy of the second ball is less by that amount. Molecular energy is transmitted in the same way from particle to particle of a solid body. This is called con- duction of heat, which, in mechanical terms, means that the particles of the body which are in motion transmit motion to those which are at rest. Only the kinetic energy which causes separation of the particles can be thus transmitted, for the force of attraction which causes contact is inherent in matter, and cannot be transmitted from one particle to another. The rate at which the transmission takes place depends upon the molecular mobility of the substance. In some substances the particles move readily by contact with others in motion, and are called good conductors of heat. Others are bad conductors, but, when once heated, they retain the heat for a greater length of time, for the same law applies to receiving and communicating motion. When energy is transmitted between the ether and solid matter, the action takes place through the molecular form of energy only. Heat rays falling upon a solid body do not produce any motion of the body as a whole, but only of its particles, among which they set up molecular motion. The same law is observed when energy is transmitted from solid matter to the ether. The motion of 24 Molecular Forces and Newtonian Laws. a solid body through the ether does not produce that wave-motion known to us as radiant heat. When a cannon ball strikes an armour plate the energy of the ball is not converted directly into etheric waves. Molecular motion is first set up in the substance of the ball by the con- cussion, and from the motion of the particles the energy is transmitted to the ether. The action is very closely allied to the production of sound. The motion of a body through the atmosphere does not generally produce sound, but very rapid vibrations do. The ether is a much rarer medium than the atmosphere, and requires still more rapid vibrations to set it in motion. The waves of ether can be approximately enumerated, and must correspond with the vibrations of the heated body by which they are produced. Also, the amount of energy lost by the heated body at every successive wave must be equal to that which is transmitted to the ether ; and since the measure of energy is the product of force into distance, it would appear that the only difference between the vibrations of a heated body and etheric waves, is, that the one is the action of a comparatively large force through a very short distance, while the other is the action of a very small force through a comparatively large distance. The force of attraction between the particles of any body is, of course, in pro- portion to its density. 7. Polarity and Elasticity of Matter. The property of matter underlying attraction is polarity. Every atom and every molecule appears to have a positive and a negative pole by means of which they are attracted towards each other. These terms positive and negative, are used without any hypothesis as Force and Energy. 25 to their nature. All we know is that attraction takes place between dissimilar poles. Since all solid matter is made up of such atoms and molecules, it may be convenient to speak of these atomic or molecular poles as magnetic points. Any body having a positive and a negative point, whatever its size, may be called a monad. Since every particle of matter is attracted towards every other particle by a force between their opposite magnetic points, it is obvious that every line of force has a positive and a negative pole the same as magnetism and electricity. The only difference is, that in the latter cases the lines of force are polarised ; that is to say, all their positive poles lie in one direction, and all their negative poles in the other. All the lines of force between the poles of a magnet lie in the same direction, but in the force of attraction between two distant bodies, such as the earth and sun, there is an equal number of lines in either direction. There is no matter, so far as known, which does not possess polarity and consequent attraction. It is mani- festly an essential property of all gravitational matter, without which it could not accumulate into solid masses. Polarity also belongs to the ether; because it transmits energy in the form of heat. But heat, as we have seen, consists of rapid interchanges of kinetic and potential energy, and there could be no such interchanges unless the ether possessed an internal force bringing the particles together after separation by the action of energy. Obviously, therefore, the ether has gravitational force according to its mass, the same as solid matter. Between similar magnetic points there is no force. If there were a force of repulsion between similar magnetic points equal to the force of attraction between dissimilar 26 Molecular Fwces and Newtonian Laws. points, no two particles of matter could ever combine. And if there were a force of repulsion less than that of attraction, it would, by the Newtonian law, be a constant quantity, which would only mean that the force of attraction is so much less. It may be safely inferred that between similar magnetic points there are no lines of force; and accordingly no such force as gravitational repulsion is known in nature. (See Note 6.) Atoms and molecules also possess the property of elasticity ; for when they collide under the force of attrac- tion, they rebound owing to the energy which they have acquired. All that is here meant by elasticity is the force by which any two particles are separated after colliding. If energy could not be converted into some other form, seeing it cannot pass out of existence, atoms would be forced apart after collision with the same energy as they collide. But the force of attraction being very great at these short distances, no sooner do the atoms rebound than they are again brought into contact. And this process of alternate separations and contacts continues until the whole energy has been dissipated by conduction and radiation. When the distance through which the force of attraction can act has been exhausted, the particles are held together by the same force in the form of cohesion. (See Note 7.) The process above described is illustrated in a rough way by the action of an ivory or an India-rubber ball when it falls upon a hard surface. The ball rebounds for a certain distance, but contact again takes place by the force of gravitation ; and this process continues till the whole energy is converted into heat. In all such cases the mechanical energy is converted into molecular energy before it assumes the form of heat waves, and we generally Force and Energy. 27 call bodies elastic in proportion to the length of time occupied by the change. Bodies in which the change of energy from the mechanical to the molecular form takes place at once, are said to be non-elastic. (See Note 8.) 8. Interchanges of Kinetic and Potential Energy. Energy is motion, and potential energy is possible motion. When energy is transmitted to any body it necessarily produces potential energy, and if that potential energy is not run down, or only partially run down, the potential energy of the body is increased. In ordinary circumstances this means expansion, for potential energy is the product of force into distance. When a bar of metal is heated — that is, when energy is transmitted to it — there is molecular action and reaction among its particles. But these are not exactly equal, for the bar expands as a whole, and that expansion means so much potential energy remaining to be run down in altered circumstances. This law applies also to the mechanical form of energy. A planet revolving round the sun has a certain kinetic energy, which, by Newton's first law of motion, tends to carry the planet away from the sun ; it has also a certain potential energy in the direction of the sun. If we suppose the sun and planet to be two particles of one body, that body is subject to expansion and contraction the same as any two particles of the heated metallic bar. The distance between the sun and planet at any given time, or the expansion of the supposed body, is that distance at which the centrifugal and centripetal forces are in equilibrium. Other than energy, and attraction acting through distance, no power capable of producing motion is known 28 Molecular Forces and Newtonian Laws. to exist in nature. We conclude, therefore, that all physical phenomena consist of interchanges of kinetic and potential energy, and that the actual condition of any body at any given time is a state of counterpoise between the opposite powers of expansion and contraction. Let us trace, by way of illustration, some of the changes which water thus undergoes. Suppose we have a piece of ice some degrees below 0° C. By the application of heat the temperature of the ice is raised to the melting point, when it begins to melt ; but there is no further accession of temperature until the whole is melted, which requires as much heat as would suffice to raise the temperature of the water to 80° C. very nearly. Under the application of more heat the tempera- ture increases from the melting point of ice to the boiling point of water, where it begins to evaporate, and the temperature remains unchanged until the whole has evaporated, which requires an amount of heat sufficient to raise the temperature about 537° C. When the whole of the water has been converted into steam, the temperature again rises by the application of heat. Let us, then, consider what happens at the melting point where the water passes out of the solid into the liquid state, and at the boiling point where it passes out of the liquid into the gaseous form. What becomes of all the heat expended in converting the ice into water at the same temperature ? By the conservation of energy, kinetic energy cannot be expended without generating an equivalent amount of potential energy. It may be inferred, therefore, that the potential energy of the water is greater than that of the ice by the amount of heat required to produce the change. This is shown to be the case by the potential energy running Force and Energy. 29 down to heat when the water is again frozen. Potential energy is the product of force into distance, so that the increase of potential energy would, in ordinary circum- stances, imply expansion of the water. This, however, is not the case, for the water shrinks by about -^ of its volume in passing out of the solid into the liquid state. The distance between molecule and molecule of the water in the liquid state is actually less than in the frozen state. The force of attraction, however, does not depend merely upon the distance of the molecules from one another, but upon the distance of their magnetic points. Every molecule is a small magnet with a positive and a negative pole, and their opposite points may be in contact while there is considerable distance between the molecules, or there may be considerable distance between the magnetic points while the molecules are arranged in compact order. We do not know the form of the molecules, but that it is some regular geometrical figure is certain from the conformation of ice crystals and snowflakes and the fern-like tracery on our window panes on a frosty morning. Let A and B be two molecules with their opposite magnetic points, n s, in contact, as we may suppose them to be arranged in the frozen state of the water. In that position there is no potential energy between them. Let A' and B' be the same two molecules as they may be supposed to be situated in the liquid state of the water, with a distance between n' s', their opposite magnetic points. Although situated more compactly than in the irozen state, there is 30 Molecular Forces and Newtonian Laws. at the same time considerable potential energy between them. The crystallised form of ice compared with the amorphous state of water leaves no room to doubt that this is the correct explanation of the phenomenon. The fact that some substances contract and others expand in freezing is thus easily accounted for by the different forms of the atoms or molecules and the position of the magnetic points with respect to their planes and angles. The expenditure of heat required to convert water into steam at the same temperature is more easily accounted for. It is merely converted into kinetic energy in another form. Water at boiling point has no pressure, but steam at the same temperature has a pressure of one atmosphere or 15 pounds to the square inch very nearly. At 100° C. the dispellent power of heat and the force of cohesion among the particles of the water are in equilibrium, and any increase of temperature drives the particles apart in the form of vapour. The equivalent of the heat thus expended is to be found in the motion of the particles, according to the kinetic theory of gases. When more heat is applied the motion of the particles, and consequently the pressure of the gas, is increased. The nature of the motion among the particles is that rapid vibration or interchange of kinetic and potential energy known as heat. The explanation above given, that the potential energy of water is due not merely to the distance between the molecules but to the distance between their magnetic points, goes far to remove the difficulty that is felt regarding chemical affinity. Owing to the exceedingly small distance through which the atoms move in forming chemical combinations, even the law of inverse sqiiares is felt to be insufficient to account for the great heat that is Force and Energy. 31 developed. But to the heat produced by the force of attraction acting through the distance between the atoms or molecules, there falls to be added the running down of the potential energy between the magnetic points of the atoms or molecules even when they are in contact. We have seen that in the case of water this is equal to an increase of 80° C. of temperature. In the freezing of water the heat is produced very gradually, and the effect is not very perceptible. When water and sulphuric acid are mixed together, or when oxygen and hydrogen are combined, the action is almost instantaneous, and the effect is very marked. But there can be no reasonable doubt that the nature of the cause is the same in all cases. Action of a similar kind, to be explained hereafter, consti- tutes the difference between magnetism and ordinary gravitation. When these movements and combinations are better understood, there will probably be no difficulty in accounting for all the facts of chemical affinity by the Newtonian laws of force and motion without assuming any other force than gravitation. 9. Mechanical Power. Every heat vibration consists of an expansion and contraction between the particles of a body; but these molecular movements are too minute to be employed for mechanical purposes. The expansion or contraction of the body as a whole may, however, be used in that way. The expansion or contraction of an iron bar by changes of temperature is an important mechanical power in the hands of the engineer, and may occasion serious damage if not carefully provided for. Since all physical pheno- mena consist of interchanges of kinetic and potential 32 Molecular Forces and Newtonian Laws. energy, that is, expansions and contractions, there can be no other kind of mechanical power. Energy may be transmitted from one body to another, but it always originates in contraction and ends in expansion. For practical purposes mechanical power can be most readily obtained by means of substances in the liquid or gaseous state,in which great changes of volume are produced by comparatively small variations of temperature. At 100° C. a cubic inch of water expands to about a cubic foot of steam, and the expansion is still more rapid above that temperature. Hence the mechanical power of steam in the cylinder of the engine. The condenser of the steam- engine affords an instance of mechanical power by contraction. The expansion of the steam by heat tends to burst out the walls of the cylinder, and the contraction of the steam by cold tends to make the walls of the condenser collapse. Hence the mechanical power by expansion in the one case and by contraction in the other. The particles of a body at any given time are in a state of equilibrium between the opposite powers of expansion and contraction, and that equilibrium is maintained under changes of temperature by the motion of the particles. When the particles are left to move freely there is no mechanical power at any given time; but if they are prevented from moving while the temperature is increased or diminished, there is a pent up mechanical power of expansion or contraction as the case may be. In the steam-boiler expansive power is stored up, and is converted into potential energy by the expansion of the steam as soon as the valve is opened. When water is subjected to heavj- pressure while the temperature is reduced below the freezing point there is stored contractive power among Force and Energy. 33 the particles of the water, which is converted into heat by the freezing of the water as soon as the pressure is removed. The water of a reservoir with a certain head, or fall, is also so much pent up contractive power, and may be converted into heat, or employed to do work by allowing it to move under the force of gravitation. Mechanical power is stored up in the steam-boiler in the form of motion among the particles of steam. That motion consists of vibrations like those between the particles of a solid body when heated, so that every vibration is an interchange of kinetic and potential energy. This is known as the kinetic theory of gases. In the case of water below the freezing point and subjected to pressure, the mechanical power is stored up in the form of supressed contraction; for, to use an Irish bull, water expands by contraction, that is to say, the volume increases by the contraction of its magnetic points. A more familiar form of stored contractive power is electricity, the nature of which will be explained hereafter. An electric-charge between two thunder-clouds, or between a thunder cloud and the earth, is so much stored con- tractive power. The discharge of steam and of electricity are characteristic of the two forms of mechanical power. Discharge of steam produces a cloud ; discharge of elec- tricity produces a spark. The one dispels the particles of matter, the other causes them to converge. Heat produces expansion, and cold, or negative heat, produces contraction. If these processes be reversed, it is obvious that the compression of matter must produce heat, and the expansion of matter increased cold, or power of contraction. This can be illustrated by a very simple appliance. Take a cylinder closed at the bottom and open at the top, and fitted with an air-tight piston. If the piston c 34 Molecular Forces and Newtonian Laws. be pressed down while the cylinder is filled with air, heat is produced by the compression of the air. If the piston be placed at the bottom of the cylinder and suddenly drawn up, the air remaining in the cylinder is expanded by the action of the piston, and the temperature is lowered. This shows that work can be performed to produce expansion or contraction at pleasure. The first is the principle of the heat engine ; the second is the principle of the electric engine : they are thus the converse of each other. Both of these forms of mechanical power cannot, how- ever, be obtained with equal facility by means of the same substance. Expansive power is most readily obtained by substances in the gaseous form, which freely admit of expansion by heat : electricity is most readily obtained by substances which lend themselves freely to polarisation, a state of matter which will be explained more particularly under the head of Magnetism. Electric power, like steam power, can be accounted for only by the Newtonian laws of force and motion. 10. Lines of Force. Every particle of matter attracts every other particle, the direction of the force being in a straight line between them ; and since attraction exists only between dissimilar magnetic points, every line of force has a positive and a negative pole. There is no sufiicient evidence of any lines of force having two positive or two negative poles with a force of repulsion between them, and the hypothesis is contrary to the law of universal gravitation. Lines of force have no relation to time. They constitute Force and Energy. 35 a fixed relation between all particles of matter, which is coeval with the particles themselves. We can calculate the time in which light or heat passes from the sun to the earth, but force does not pass at all; it exists between them. The intensity of force between any two particles varies according to distance, but is not affected by time. At the same distance the force is always the same. Any interruption of this law would imply a creation or destruc- tion of energy. Heat modifies the force of attraction between particles of matter only by modifying the distance between them. Solar rays falling upon a cloud of vapour cause expansion and therefore diminish the force of attraction among its particles ; but if the temperature of the sun were increased ten-fold there would be no change in the force of attraction between it and the earth, because the distance between them reiriains unchanged. (See Note 9). A force of attraction between any two bodies, or particles ■of matter, implies continuity along the whole line. One broken link in a chain, or one gap, however small, in a magnetic circuit, renders the action of force along that line impossible. This is Faraday's law of " Induction by contiguous particles.'' The term induction is used to denote a certain form of electric and magnetic force ; but the law is applicable to force in all its forms. Neither ■can force act nor energy be transmitted between two bodies without some continuous material medium between them; in other words, the action is by contiguous particles. The universe, in so far as known to us, consists ■of one continuous material system ; hence the action of force and energy between all bodies, however remote from one another. If there were two material systems without continuity, there could be no force between a 36 Molecular Forces and Newtonian Laws. body in the one and another body in the other. Even if both bodies were glowing at a white heat, there would be a wall of absolute darkness between them. All lines of force are independent of one another. A change in the lines of force between any two particles of matter does not affect the lines of force between them and all other particles. The gravitation of a candle is the same before, during, and after combustion, notwithstanding the change in the lines of force between its own particles and others entering into combination with them. These changes do not affect the lines of force between the substance of the candle and the earth. This shows that attraction is a force between particle and particle, and that the total gravitational force between any two bodies is the sum of all the forces between their respective particles. The contractive force inherent in matter resides in all its particles alike, and acts through contiguous particles along the whole line between them. Lines of force are not interrupted by the passage through them of any solid body. The force of attraction between the sun and moon is not affected by an eclipse of the latter body, although at that time the earth passes through the lines of force between them. The phenom- enon is accounted for by Faraday's law. There is continuity between the two bodies, and the force of attraction acts by contiguous particles along the whole line. The fact that the line consists partly of ether and partly of solid matter does not affect the intensity of the force, because the force acts by means of the intervening medium, and is not obstructed by it. There is, indeed, a much greater force tending to bring the sun and moon together when the earth is in a direct line between them than when the space is occupied by ether alone, but that Force and Energy. 37 increased force consists of the lines of force between the earth and the two heavenly bodies, and has no connection with the Knes of force between the sun and moon, except that it acts in the same direction. From these considerations it follows that the force of attraction between any two bodies is equal at equal distances. The force of attraction is neither increased nor diminished by the contiguous particles through which it acts, for that would imply a creation or destruction of energy. Since force is inherent in matter, or — which is the same thing — exists between all particles of matter, it can never change, so long as the constitution of matter remains unchanged. Force, therefore, can never be resisted nor become exhausted. Motion can be resisted, but not force. And since it acts through contiguous particles, the force between any two bodies is the same at the same distance, whether the intervening space be occupied by ether or solid matter, and whether the intervening substance be at rest or in motion. This law is so obvious from the familiar facts of gravitation that no experiments are necessary to prove it. The table does not resist the lines of force between my inkstand and the earth, but it resists the motion of the inkstand. From the facts above stated it follows that the force of attraction between two bodies is inversely as the square of the distance. Since force acts equally in all directions, and is equal at equal distances, the surface of a sphere of which any given particle is the centre, is an equipotential area in so far as the force of that particle is concerned. And since force is not affected by the number of particles through which it acts, the total force at the surface of any sphere of which the particle is the centre is the same, whatever the size of the sphere. In other words, the force 38 Molecular Forces and Newtonian Laws. is inversely as the area over which it is distributed. Now, this is the law of inverse squares. Let A B D be the surface of any sphere of which the particle C is the centre; also let d be the radius of the sphere, and / the force of attrac- tion between C and any particle A, on the surface of the sphere. The force between C and every par- ticle on the surface of the sphere is equal. Let us call the sum of all these forces, unity; then / is equal to unity, divided by the number of particles on the surface of the sphere. But the number of particles is in proportion to the surface, and the surface is in proportion to the square of the radius ; therefore, /= -^ that is, the force between any two particles is inversely as the square of the distance between them. If the medium is more dense at one part of the surface than another, as from B to D, the particle C moves in that direction, because there is a greater number of particles at the same distance ; but the force between particle and particle is the same, so that the law of inverse squares holds good for all variations in the density of the surrounding medium. It is to be observed that the force of attraction is between the positive and negative points of the monad C, and that all surrounding matter consists of the contiguous particles through which the force acts, in accordance with Faraday's law. In this way every particle of matter Force and Energy. 39 attracts every other particle, and all the lines of force are distinct from one another. The force between the magnetic points of every monad acts through and attracts every other monad in the universe. The correctness of this view will be more apparent when we come to treat of magnetic attraction. 11. One Law for all Masses and Distances. It may be assumed as an axiom in physics that matter follows the same laws, irrespective of mass and distance. Great and small are only' relative terms. Compared with the extent of matter as seen in the depths of the milky way, or in the remote nebulae, our solar system consists only of a few atoms revolving in a small comer of space. Yet, from these great and remote masses of matter down to the minutest particles that can be weighed, and at the shortest distances that can be measured, the laws of force and motion are the same, and the interchanges of kinetic and potential energy take place in the same order. No limit of mass or distance can be fixed at which a change in the law takes place, nor any sufficient reason assigned for such a change, because the known laws sufficiently account for all observed phenomena. (See Note 10.) Eelying on this principle, we may, without hesitation, trace the action of molecular forces and the motion of material atoms, although the masses and distances are too minute for observation or measurement. Having found any law to be invariable for all measurable quantities, we can hardly err in applying the same law to quantities that are infinitesimal. Kinetic energy is never produced but by the running down of potential energy, and is never expended without producing the same ampunt of energy in the potential form. This law applies equally to the 40 Molecular Forces and Newtonian Laws. stars of a galaxy and to the molecules of a drop of water. Nature has no secrets. She works in the chemist's laboratory by the same laws as she exhibits daily before the eyes of every observer. There is apparently no distinction between ether and solid matter in respect of force and motion. Force acts through ether by the law of contiguous particles, the same as through solid matter; and heat when transmitted to the ether consists of expansions and contractions like the heat of any other gas. Neither is there any reason to suppose that radiwm, is an exception to these laws. Our knowledge of that substance is still in its infancy, but, when its nature has been more fully investigated, the action of its particles will, no doubt, find its explanation in the Newtonian laws. These extremely minute sub- divisions of matter are regulated by the same laws which govern the grosser forms of matter. All material atoms possess geometrical forms, as is shown by their crystallisa- tion ; and it is more than probable that they are made up of still smaller, perhaps polarised, particles. The time has come when it is necessary to go beyond atoms in studying the constitution of matter. Perhaps we may yet have to fall back upon the endless divisibility of matter, as taught by Anaxagoras a generation before the atomic theory was propounded by Democritus. (See Note 11.) CHAPTEE II. MAGNETISM. 1. Magnetics and Non-Magnetics. SUBSTANCES are divided magnetically into those which admit of magnetisation and those which do not. The distinction depends upon some kind of mole- cular mobility. When a substance is magnetised a change takes place in the position of its atoms or molecules. If the magnetising force is an electric current, a metallic clink is audible within an iron bar when the current is turned on and the atoms assume the magnetised position, and a similar sound is again heard when the current is turned off, and the atoms resume their ordinary position. It has also been observed that magnetic force acts along the whole length of a magnetic substance, whatever its form, without any appreciable change of intensity : through a non-magnetic substance the force acts in straight lines, and the intensity is inversely as the square of the distance. For this reason Faraday characterised them as para- m.agnetics and diamagnetics. The test of these properties is, that paramagnetics set themselves axially — or in the direction of their longest axis — between the poles of a magnet. Diamagnetics set themselves equatorially , or in the direction of their shortest axis. If N S be two magnetic poles, Fe a small bar of iron, and Cu a. small 42 Molecular Forces and Newtonian Laws. Cu EI bar of copper, the figure illustrates the characteristic position of the two classes of sub- stances between ^ the poles of a magnet ; iron being magnetic, and copper non-magnetic. The number of magnetic substances is very considerable. It includes iron in its various forms, nickel, cobalt, and a number of other metals; also oxygen and some other non-metallic substances. Most of these, however, possess the magnetic property in a very limited degree only. By far the most important substances of this class are iron and oxygen; and their magnetic property fulfils an' important function, both in art and in the economy of nature. (See Note 12.) The terms magnetic and non-magnetic are probably relative only. Iron and some other substances are called magnetic because they possess the property in a high degree; copper and other substances are called non- magnetic because they possess it in a very low degree only. When the force between two magnetic poles acts through a non-magnetic medium, it is called a magnetic field, and the strength of the field is in proportion to the magnetic property of the medium. If the field consists of a perfectly non-magnetic substance, the force is inversely as the square of the distance ; if it possesses any degree of the magnetic property, the force is greater. Atmospheric air, being largely composed of free oxygen, is magnetic, and forms a strong field of force. Although magnetic substances are fairly abundant in nature, no substance in its natural state possesses magnetic force. The lodestone, or natural magnet, is a species of Magnetism. 43 iron-ore, which, like hard steel, has the property of retaining magnetisation for a great length of time, and is magnetised by the force known as terrestrial magnetism. Oxygen also possesses this property of retaining magnetisa- tion. Soft iron parts with magnetisation instantly the magnetising force is withdrawn. Hereafter we shall trace the origin of magnetic force to natural causes, but meantime it will be sufficient to refer it to already existing magnets. 2. Magnetism a Foem of Gravitation. Whatever the precise nature of magnetism, it is mani- festly a force which belongs to the substance of the magnet, and always resides in it. A magnetised steel bar retains its magnetic force for years, or even centuries, and continues to produce energy during all that time without perceptible diminution. This would be impossible if the force were imparted to the magnet by the process of magnetisation. In whatever form the energy might be stored up, it would gradually become exhausted by the action of the magnet. We conclude, therefore, that magnetism is a modified form of that inherent force of attraction which exists in all gravitational matter. The action of magnetic force is the same as that of gravitation. It produces energy only by acting through distance; and when the distance is exhausted, no more energy can be produced until separation has again been made by the action of kinetic energy. When the keeper of a magnet is removed from contact with the poles, there is potential energy amounting to the product of the force by the distance, and when that runs down it produces an equivalent amount of kinetic energy. Thus, the Newtonian law of action and reaction applies to magnetic force the same as to gravitational force. 44 Molecular Forces and Newtonian Laws. For the same amount of matter, magnetic force is enormously great compared with gravitation. The force between the poles of a small magnet will sustain a pound weight, whereas the gravitational force between two blocks of metal of a ton each, suspended in the immediate vicinity of each other, is scarcely perceptible. Now, this great force cannot be due to any increase in the force of attraction inherent in the particles of the magnet, for that would mean a creation of energy. Neither is there any change in the distance between the particles sufficient to account for the great change in the force between them. We infer, therefore, that the great increase of force is due to the position into which the particles are put in the process of magnetisation. We have seen that a change in the position of the molecules of water, produced by the process of freezing, is sufficient to raise the temperature of the water 80° C, and there seems no reason to doubt that the great magnetic force is produced in the same way. We conclude, therefore, that the magnetism of an iron bar is due to the ordinary force of gravitation between the particles, modified by the peculiar position into which they are put in the process of magnetisation. (See Note 13.) The celebrated theory of Ampere accounts for the magnetic force of an iron bar by supposing that an electric current flows round every atom in the substance of the iron. This accords with the ascertained fact that an electric current magnetises an iron or steel bar in its immediate vicinity. But the existence of such currents within the substance of an iron bar is at once incredible and impossible — incredible, because it implies the insulation of the currents from the iron and from one another, and, therefore, the existence of another substance different in its properties from iron; impossible, because it is Magnetism.. 45 contrary to the conservation of energy. An electric current can be maintained only by the expenditure of energy. Even Clerk Maxwell's hypothesis of perfect conductivity does not obviate this objection; for although it might account for the iron not becoming heated by the action of the currents, it does not account for the energy produced by the magnetic force. It seems, moreover, to have been entirely overlooked, in connection with this theory, that when an electric circuit is completed discharge takes place, and the whole potential energy of the current runs down to heat. By this known law of electricity the existence of these electric circuits is an impossibility. This ingenious theory belongs entirely to' the sphere of imagination — the wonder is that it should ever have obtained a place in science. (See Note 14.) 3. Polarisation of Magnetics. The peculiar arrangement of the atoms in a magnetised substance consists in polarisation ; that is to say, all the positive magnetic points lie in one direction and the negative points in the other, so that alternate positive and negative points are in contact throughout the whole substance. This may be inferred without much doubt from the fact that the whole positive element of the magnetic force is exhibited at one extremity of the magnet, and the whole negative element at the other. For a positive proof of this point, however, we must wait until we come to Terrestrial Magnetism. We cannot get inside an iron magnet to ascertain how the atoms lie, but it will be shown hereafter that the atmosphere is a great magnet, and as we can get inside that magnet, we can test by means of a magnetic needle the direction in which the 46 Molecular Forces and Newtonian Laws. magnetised atoms lie. This will be understood from the accompanying figure, which is sup- posed to represent a small section of magnetised atmospheric air. The magnetised needle shown in the centre of the figure necessarily lies in the same direction as the magnetised atoms, for in any other position the poles of the needle would be towards similar poles of the adjacent particles, and there would be a directive force turning the needle into the same direction as the particles of the surrounding element. When the molecules of water are polarised, or some- thing analogous to it, g^eat heat is produced ; and after the heat has been dissipated by conduction or radiation, the molecules are held together in the solid state by a strong force of cohesion. When a magnetic substance, such as an iron bar, is polarised, very little heat or change of cohesion is observed ; for there seems to be very little difference of cohesion in a bar of iron in the magnetised and unmagnetised states. But, instead of increased cohesion, the force of the atoms acts along the polarised lines, and is exhibited at the extremities of the bar. That this happens in the case of magnetised substances can be shown by means of a number of small magnets. Let a great number of small magnets, n s, be arranged as in the figure, so that polarised lines are formed throughout the whole length of the bar. The combined force of all these little magnets is exhibited at N S, the extremities of the bar. The n an sn sn Magnetism. 47 effect is the same, however small the magnets are, and it could make no difference if each magnet consisted of a single atom, because every magnet is only a succession of such atoms. That this is the nature of a magnet is shown by the fact that when it is broken to pieces the smallest fragment is a complete magnet in itself From the foregoing conclusions it follows that a magnet forms a single monad ; that is to say, it has one positive and one negative pole, the same as a single atom. Also, since its poles, or magnetic points, are at its extremities, the whole length of the magnet, whatever it may be, counts only a point in so far as the action of magnetic force is con- cerned. This can be proved by a very simple experiment. Let N S be the poles of a magnet, and S' N' a piece of soft iron used as a keeper. When the keeper is placed as in the r^- ^ figure, the force between N ^^ ~^" and S' is the same as if S had been brought so much nearer N, so that the keeper from S' to S counts nothing in respect of the magnetic force. When the keeper touches both poles of the magnet the force is the same as if the poles were in contact, and the whole length of the keeper is only a point in respect of the force. This accounts for the greatness of magnetic force com- pared with gravitation. The inherent force of the atoms is not increased, neither is the distance between them altered ; but, since the distance along the polarised lines is only a point, the effect is the same as if distant particles were brought into contact. The forces of the polarised particles act in series along the same lines, whereas in unpolarised 48 Molecular Forces and Newtonian Laws. matter they radiate and are inversely as the square of the distance. Magnetism is thus in strict accordance with the Newtonian law — that force varies according to distance only. When a substance is magnetised to its utmost capacity, it is commonly said to be magnetised to saturation, from the old theory that magnetism is a fluid. The correct meaning appears to be, that every particle is brought fully into the polarised position. The tendency of the particles is to fall into their natural position unless they are held in the polarised state, either by the magnetising force, as in the case of soft iron, or by the nature of the substance itself as in the case of hard steel. 4. Magnetism and Gravitation. Gravitation is a force of attraction between all particles of matter according to their mass. Magnetism is a special force of attraction between the particles of a magnetic substance, caused by their polarisation and the con- centration of the force along the polarised lines. But we have seen that a change in the force of attrac+ion between any two bodies or particles of matter does not affect the force between them and all other bodies or particles. Hence the magnetisation of an iron bar does not alter its gravi- tation ; just as the gravitation of a candle is not altered by its combustion. For this reason also a magnet does not attract, magnetically, a non-magnetic substance. A magnetic substance, however, is attracted, because it becomes magnetised, which has the same effect as if all the positive magnetic points of the substance were collected at the end next the negative pole of the magnet, and all the negative points at the end next the positive pole. The magnetic substance is, therefore, attracted towards the nearer pole of the magnet. Magnetism. 49 When lines of magnetic force act through a magnetic substance, they are of uniform intensity throughout its whole length, because the whole substance forms a monad whose poles are equal but of opposite sign. And the lines act along the substance, whatever its form. The keeper of a magnet may be straight or bent into any shape ; the force acts through it all the same. Through a non- magnetic substance, magnetic force acts in straight lines, and its intensity is inversely as the square of the distance like gravitational force. This shows that magnetic force radiates through a not-magnetic medium so that it becomes distributed over a greater area. No part of the force is lost in passing through the diamagnetic, for force can never be lost nor become expended. Neither would it be correct to say that it encounters resistance, for it acts by means of contiguous particles, and is not resisted by them. But the force becomes distributed over a greater area in proportion to the distance through which it acts in the diamagnetic medium, and when measured along anj- particular line its intensitj' is inversely as the square of the distance. This law is illustrated by the accompanying figure. Let N S be the poles of a magnet situated in a non-magnetic medium. From S to N the force acts through the magnet along the polarised lines, and is of bhe same inten- sity throughout the whole distance, because it is not distributed over any wider area. From 50 Molecular Forces and Newtonian Laws. N to S, however, through the non-magnetic medium, the force radiates as shown by the small lines, so that the intensity of the force at any point varies as the square of the distance inverse. The magnet is a monad, or atom on a large scale, and has two poles from which force radiates, the same as from every material atom. If a small bar of iron, A B, be placed between the poles of the magnet, it becomes magnetised, and the radiating lines of force form a couple which tends to turn the bar into the direction of the line, N S. This is the explanation of the fact that a magnetic substance sets itself in the axial direction between the poles of a magnet. The reason why a non-magnetic substance sets itself equatorially will be explained under the head of " Diamagnetism." When a magnetised needle is used instead of a small bar of soft iron, the effect is the same, except that the force to be taken into account is the product of the strengths of the two magnets. When the iron bar has set itself axially between the two. poles of the magnet, the distance between them is shortened by the length of the bar, in so far as the magnetic force is concerned, because the bar is only a point, and the intensity of the force is increased accordingly. In like manner, when any two atoms of the intervening medium become polarised, the line of force through that point is shortened, and the intensity of the magnetic force thereby increased. The line along which the greatest amount of polarisation takes place is the line of greatest intensity. There are probably very few substances in which absolutely no polarisation takes place. The force along any line between two magnetic poles is directly as the polarisation, and inversely as the dispersion of the Magnetism. 51 force. Along a perfect magnetic substance there is no dispersion, and along a perfect non-magnetic substance there is no polarisation. Gravitation always acts in straight lines, but this is not the case with magnetic force, which deviates to any extent from a straight line if there is polarisation along the line. In gravitation there is no polarisation ; the length of all the monads is infinitesimal, and the force equally distributed through all substances. Hence, the force between any two points is in a straight line, and its intensity is inversely as the square of the distance. 5. Magnetic Circuit. From the nature of polarisation, it is obvious that magnetic force can be complete only in circuit ; for then ■only can there be continuous contact between positive and negative points throughout the whole line of force. Such a circuit has a positive and a negative direction, but no poles ; and if composed of a uniform bar of homogeneous metal, has no attraction for any external substance, the force at every point in the circuit being between equal and opposite atomic poles. A horse-shoe magnet, having its poles connected by a keeper of soft iron, forms such a circuit. If perfectly constructed, it might be laid among iron filings without any of them adhering to it. There is no motion in a magnetic circuit; for, if the particles of the magnet were in motion, by the conservation of energy, heat would be produced. But a magnet, how- ever strong, produces no heat. And there can be no other kind of motion. Force does not move : it is the bodies between which force acts that move. Formerly scientists thought of a magnetic fluid which might be supposed to move ; but that idea has been abandoned. Although the 52 Molecular Forces and Newtonian Laws. term is still retained by some authors, it is used only to fix the idea in speaking of something the nature of which is unknown. But the term force is all that is necessary in speaking of magnetism, and that term never implies motion. Force produces motion but does not itself move. Force acting upon particles of matter after the distance through which it can act has been exhausted, is cohesion ; and of this nature is a magnetic circuit. Polarisation of the atoms, or molecules, of most substances produces great rigidity between particle and particle ; but the polarisation of a magnetic substance produces a great force of attraction along the whole length of the polarised lines. The force being circular, can produce contraction only ; and when the distance is exhausted, there can be no more motion until the particles are separated by the application of energy. But this is the law of all cohesion, so that magnetism is no exception to the law of action and reaction, and requires no mysterious element to account for it any more than the freezing of water or the crystallisation of sugar. A common magnet is a part of a magnetic circuit which is completed through the surrounding non-magnetic medium. Thepoints at which the lines of force pass out of the magnet into the non- magnetic medium are called the poles of the magnet, and the non-magnetic substance is the field of force between the poles. In that field the remainder of the circuit lies, the positive and negative directions being the same as those of the magnet. This can be shown by calling Magnetism. 53 attention to a familiar fact. Let N S be the poles of a horse-shoe magnet, and A A' A" a small magnetic needle placed in different positions in the field of force. Whether the needle touches either pole, or is placed apart from both, it always lies in the direction of the magnetic circuit. If the magnet consisted of air instead of steel, so that the needle could be carried through it, the direction of the needle would be the same while it was carried round the whole circuit. The reader will readily see in this the explanation of the direction of the needle under the influence of terrestrial magnetic force ; but the subject will come under our notice more particularly hereafter. The strength of the magnetic force is the same through- out the whole circuit, whether it lies in the magnet or in the field of force. In the latter case it is distributed over a wider area ; but if all the lines be taken into account, their sum is the same as the force through the magnet. To suppose that the magnetic force could be greater at one part of the circuit than another, is the same thing as to suppose that the tension of a chain could be greater on one link than another, or that action and reaction could be unequal. (See Note 15.) 6. Magnetic "Induction." When a piece of soft iron is brought near one of the poles of a magnet, the iron is magnetised, its pole next the magnet being of opposite sign to that pole of the magnet. This phenomenon is called magnetic iTiduction. In describing this phenomenon the action of the second pole of the magnet is generally overlooked, as if the effect were due to the nearer pole only. But there can he no force, and therefore no magnetic action, except between 54 Molecular Foives and Newtonian Laws. two magnetic poles. Induction is caused by the action of the magnetic lines through the field of force, and in accordance with the law of inverse squares, the iron moves towards the nearer pole. Let N, S, be the poles of a magnet, and P a small particle of soft iron in a direct line between them. Also, let a be the distance between N and P, and b the distance between P and S, the length of the particle being disregarded. By the law of inverse squares the force tending to carry the particle towards N, is, -\, and towards S, -^, the whole strength of the magnet being taken as imity. Since these forces are in opposite directions, the actual force tending to move the particle is " ^,.^ . It is to be observed that the positive direction of motion is towards S, that being the positive direction of the magnetic circuit. If a is greater than b the particle moves in the positive direction, and if less, in the negative direction. The magnetisation of the particle of iron depends upon its length, because the distance between the magnetic poles is diminished to that extent. But the rule for the motion of the bar is the same whatever its length ; because, while the distance between N and S is virtually diminished by the length of the bar, the ratio of the forces in the positive and negative directions is unaltered. When a magnetised bar forms a complete circuit, the whole magnetic force lies between particle and particle along the bar. Theie are no lines of force between different points of the bar through the surrounding Magnetism. 55 medium. But when the magnetised bar forms only part of a circuit, the magnetic circuit is completed by lines of force through the diamagnetic medium. These lines radiate in all directions, so that the force measured along an}' particular line is inversely as the square of the distance ; but the sum of all these lines is equal to the total force through the metallic bar. These radiating lines of force exist not only between the extremities of the magnetised bar but between every point in the positive and every point in the negative arm of the bar. There is, therefore, only one point in the magnet where the whole force of the magnetic circuit lies within the bar, and that point is called the equator of the magnet. It is not necessarily at the centre of the bar, for the metal may be uneven, or it may not be uniformly magnetised. But it is always at the centre of magnetisation, so that the total positive element of the force from the equator to one extremity of the bar is equal to the total negative element to the other extremity. Let N S be a horse-shoe magnet, E the magnetic equator, and L any point in the magnet between E and N. At E the whole force of the circuit lies within the magnet, but at L there are lines of force to every point in the negative arm of the magnet from E to S. This can be seen by placing a small magnetised needle, or a piece of soft iron, anywhere with- in the concavitj' of the magnet. At every point, therefore, in the magnet, from S to E and from E to N, the total force is distributed into two components. 56 Molecular Forces and Newtonian Laws. one along the magnet towards N, and the other, consisting of all the lines, through the diamagnetic towards the opposite arm of the magnet. The first of these is called the horizontal, and the second the dipping force of the magnet. The terms are ilori\ed from the phenomena of terrestrial magnetism, but, as will be shown hereafter, the action of the force is the same in both cases. The lines of force between the arms of the magnet increase in intensity from the magnetic equator to the magnetic poles. At E there are no such lines, because the whole force lies within ^th.e magnet ; at N and S they reach their greatest intensity, because there is no force along the magnet at these points. Thus, the lines vary in intensity from zero, at E, to a maximum at N and S. This can be seen by placing a magnet among iron filings. These adhere to the magnet in great numbers at the poles, but diminish in number towards the equator, where there are none. This shows that induction is not due to one pole of the magnet, but to the lines of force through the diamagnetic between the two poles. When the two poles are connected by a piece of soft iron the filings drop off, because the whole force of the magnet then lies through the iron circuit. There are no lines through the diamagnetic to cause induction. We have seen that a small iron bar, when magnetised by induction, sets itself in the axial position if plaeud between the poles of the magnet. We shall now consider the direction of the bar when placed in any position whatever, with reference to the magnetic poles. Let N S be two magnetic poles, and S' N' a small bar of soft iron lying anywhere in the field of force, its middle point being P. Join N S', N P, PS, N' S, and draw Magnetism. 57 PA, bisecting the angle NFS. The direction of the line of force through the bar is N S' N' S. The force along N S' not only tends to carry the bar in the direction of N, but also forms a couple which tends to set the bar in the direction N P. In like manner the force along N' S forms a couple which tends to set the bar in the direction P S. Let the mo- ments of these couples be m and n respectively. Since the couples are in opposite directions, m being left- hand, and n right-hand, the angles N P S' and S P N' are proportional to n and m ; that is, NP,S' SPxN" The bar comes to rest in the position where in and n are equal, and therefore the angle N P S' is equal to the angle S P N'. The whole angle, A P S', is, therefore, equal to the whole angle, A P N' ; that is, the position of the bar is at right angles to the bisector of the angle, between the polar distances. It can be shown, either by simple measurement or by a mathematical demonstration, that of all possible positions ■of the bar S' N', the perimeter N S> N' S is least when S' N' is at right angles to A P. The position of an iron bar, therefore, when magnetised by induction, is such, that it makes the line of force between the poles the least possible, and therefore the magnetic force along that line the greatest possible. In the case before us the line of force is shortened by the difference between N P -f- P S and N S' + N'S. The length of the bar counts nothing. {See Note 16.) 58 MolecuLar Forces and Newtonian Laivs. 7. CONVECTIVE AND DIRECTIVE FORCE. The action of a magnet upon a fragment of iron, or upon a small magnetised needle, is twofold. The fragment of iron is carried, as a whole, towards the nearer pole of the magnet. This may be called the convective force of the magnet. The law is the same as that by which an aerolite is carried towards the earth or moon, according as the attraction of either body is the greater. The only difference is, that the force is polarised in the one case, and not in the other. The direction or posture in which the fragment of iron is carried towards the nearer pole of the magnet is regulated by the law that the direction of the particle is always such as to make the distance through it between the poles of the magnet the least possible. This may be called the directive force of the magnet. It is a couple, because the magnetic force acts only at the ends of the iron fragment. The reason of this remarkable fact is, that a magnetised body is the same, in respect of magnetic force, as if all its positive magnetic points were accumulated at one extremity and all its negative points at the other. The action of these two forces may be expressed by the following rule : — The convective force, both as to its direc- tion and intensity, is the resultant of the two polar forces ; and the position of the fragment of iron, or small magne- tised needle, is tangential to an ellipse of which the poles of the magnet are the foci. Let N S be the poles of a magnet, and P a small particle of soft iron placed in any position whatever with respect to the magnetic poles. Join N P and P S, and bisect the angle, N P S, by the line, P A. Also describe an ellipse, B P C, of which N and 8 are the foci. The particle P, Magnetism. 59 moves towards S, the nearer pole of the magnet, and its p' direction is tangential to the ellipse, its positive pole being towards the negative pole of the magnet and vice versa. The resultant of the polar forces along N P and P S lies within the angle, N P S, but the motion of the particle is not in a straight line, because the ratio of the two component forces varies at every point along the line of the resultant. The particle therefore describes a curve from P to S, which can be easily traced, because its direction at any point depends only upon the polar distances. If the particle were situated at P', where the lines P' N and P' S would form the sides of an isosceles triangle, it would move in a straight line to D, where it would remain in (unstable) equilibrium. The poles of the magnet would in that case be equi-distant from the particle at every point along the whole line of motion. With regard to the direction or posture in which the particle is carried from P to S, we have seen that it is alwa)'s at right angles to a line bisecting the angle between the polar distances — that is, the line P A. But it is a well-known property of an ellipse that a line at right angles to the bisector of the angle between the focal distances is tangential to the ellipse. The direction, therefore, of the particle P, is tangential to the ellipse APB. 60 Molecular Forces and Newtonian Laws. In the extreme case in which the particle lies in a straight line joining the poles of the magnet, or in that line produced, the convective force is the sum or difference of the two polar forces, and the direction of the particle is tangential to an ellipse of which the minor axis has vanished. The action of convective and directive force is illustrated in a very striking manner by the curves formed by iron filings on a sheet of paper over the poles of a magnet. If the par- ticles were perfectly free to move, they would be instantly can-ied, each to that pole of the magnet nearest to it. But, owing to the friction of the paper, they are arrested in their course,and wehaveatableauof the particles in theirmarching order. Hence the series of ellipses formed by the iron filings. These ellipses gave Faraday the impression that mag- netic forces act in curves. But the curves do not represent lines of force at all, but only the direction or posture of the moving particles. The line of force for every particle is from the positive pole of the magnet in a direct line to the negative pole of the particle, thence through the particle at right angles to the bisector of the angle between the polar distances, and from the positive pole of the particle in a direct line to the negative pole of the magnet. This can be easily seen by observing the movement of any particular particle when the paper is gently sjhaken. It does not move along the circumference of an ellipse, but falls out of one ellipse into another, describing a curve of its own, unless the focal distances form the sides of an isosceles triangle in which case the particle moves in a straight line to the central point between the poles of the magnet. 8. No Magnetic Repulsion. From the foregoing conclusions it follows that there can be no magnetic repulsion. Such a force enuld neither be Magnetism. 61 equal to, nor greater than, the force of attraction ; for then a small magnetised needle between the poles of a magnet would either not move at all, or it would move away from the nearer pole of the magnet. But neither can there be a force of repulsion less than attraction ; for in that case the needle would not lie tangential to an ellipse of which the two magnetic poles are the foci. Repulsion is alleged to act between the similar poles of magnets, and since the distance between the similar poles of the magnet and magnetised needle differs from the distance between their dissimilar poles, the force of repulsion would cause the needle to lie at a different angle to the circumference of the ellipse. There cannot, therefore, be a force of repulsion distinct from the force of attraction. If there is repulsion at all -it can only mean that the force of attraction is less by that amount ; and this is not a question of two forces but of the magnitude of one force. The force of every magnet is a complete circuit, and when any two magnets are placed with their poles in contact they form a common circuit the strength of which is the algebraic sum of the two circuits. Let N S and W S' be two magnets, the strength of the former being F when the poles are in contact or connected by a magnetic substance, the strength of the latter being F'. When the magnets are placed with their dissimilar poles in contact, as in the figure, the strength of the common circuit is F + F'. If one of the magnets be reversed, so that similar poles are 62 Molecular Forces and Newtonian Laws. in contact, the strength of the common circuit is F — F' ; because the circuits tend to neutralise each other. If two of the poles are in contact and the other two separated by a distance cl, the strength of the common circuit is -^-, according as the poles in contact are dissimilar or similar. When all the poles are apart, and the length of the magnets, that is, the distance between their poles, being I, -the strengths of the circuits are-jj-and-yrj-' respectively. These forces may be represented by the symbols f and f. It is to be observed that one pole of a magnetic force cannot be expressed by any rational quantity, because there is no force except between two poles. When the force of a magnet is /, each of the poles is represented by the imaginary quantity or surd ± «/-/■ When two magnets are parallel to each other the circuits are completed through the diaraagnetic, and tend to form a common circuit the same as when in contact ; but the forces act through the diamag- netic, according to the law of inverse squares. Let N S and N' S' be two parallel magnets at a distance, d, from each other, their strengths being / and /' respectively. When the dissimilar poles are towards each other the magnets strengthen each other by induction, and the two circuits are / + =4 and /' + -^ ; and the force tending to bring the two magnets into contact — that is, their product divided by the square of the distance between them — is d? ^ d^ ■ ■ ■ (!)• N d N' ^ S' MagnetisTTi. 63 Since / and /' are in the same direction they may both be regarded as positive, and

3'id the force tending to bring the magnets together is g3 X d3 . ■ • (,^> Since / is greater than /', and c?^ a positive quantity greater than unity — for -^ is less than f f — ^the first factor of the force (2) is positive for all values of d. If a value of d, say, dj, be taken such that / = /' c?^, the second factor of (2) vanishes, and consequently the whole force tending to bring the magnets together vanishes. The explanation is, that at distance, d^, the magnet, N S, neutralises the weaker magnet, and there is no attraction between them. The effect is the same as if the magnet, N' S' consisted of diamagnetic matter. If d, be less than d^, say, d^, the whole force (2) is positive, and the magnets are attracted towards each other. The explanation is, that at distance, d^, the magnet, N' S', is not merely neutralised, but reversed ; and, since there are two circuits in the same direction, the magnets are attracted towards each other. If the distance between the magnets is greater than 64 Molecular Forces and Newtonian Laws. d„ say, c/.„ the force (2) is negative, which means that at distance, d^, the magnets are attracted in opposite directions. The nature of this phenomenon we shall now explain. Let N S and N' S' be two parallel magnets of equal strength, and placed with their similar poles in the same direction. In this case , .. ... / the force tending to ' bring the two magnets into contact is negative at all distances, because the magnets, being of equal strength, can neutralise each other at the point of contact only. Join N N' and produce to A and A' ; also join S S' and produce to B and B'. Lines of force radiate in all directions from each of the magnetic poles through the diamagnetic medium. But every line of force radiating from N can be resolved into two components, one along the line A A', and the other at right angles to it. So also every line of force radiating from N'. Now, the algebraic sum of all the com- ponents at right angles to A A' is zero ; because for every point from which there is a force at right angles to A A', there is another point from which the force is equal and opposite. The algebraic sum of all the component forces along A A' from N to N' is also zero ; because the components of all the forces radiating from N are in the direction of A', and the components of all the forces radiating from N' are in the opposite direction, so that their algebraic sum is zero. From N, however, there is a force in the direction A, because the components of the lines of force from both N and N' are in that direction. So also there is a force from N' in the direction of A'. Magnetism. 65 The forces radiating from S and S' are the same as from N and N', but in the negative direction. There is there- fore a force along B B' in the direction from S to B, and in the direction from S' to B', but between S and S' the force is zero, because the component forces are equal and opposite. Lines of magnetic force magnetise by induction any magnetic substance through which they pass; and the atmosphere is such a substance, because it is largely com- posed of free oxygen, which is paramagnetic. In the space between the two magnets there is no magnetisation, because the forces neutralise each other; but in the space outside the magnets the atmosphere is magnetised in the opposite direction to that of the magnets ; and since mag- nets always attract each other when their opposite poles are towards each other, the two magnets are attracted by the magnetised air. But there is no magnetisation in the space between the magnets, so that they are attracted away from each other. In terms of the formula, the force bringing the magnets together is negative. The law above stated can be illustrated by placing a small magnetised needle on a smooth surface near the poles of a strong horse-shoe magnet. Let NS be the magnet, and N' S' the small needle, N' the strength of the magnet being/; and that of the needle /'. If the similar poles are in oppo- 5' site directions, the needle is attracted to the magnet at all distances ; but if the similar poles are in the same direction, as shown in E 66 Molecular Forces and Newtonian Laws. the figure, when the needle is placed at a distance, d, such that ^=/', there is no motion, because the magneti- sation of the needle is neutralised by the magnet. When the distance is less than d, the needle moves towards the magnet, because its magnetisation is reversed. When the distance is greater than d, the needle moves away from the magnet as if it were repelled. The reason is, that the atmosphere beyond the neutral point is magnetised oppositely to the needle, which is therefore attracted in that direction. For the same reason, the magnet is attracted in the opposite direction, but owing to its great weight and the smallness of the force, the motion is scarcely perceptible. This is the force which has been mistaken for repulsion. The case is one in which appearances are misleading, just as the ascending of smoke appears at first sight to be an exception to the law of gravitation. But the critical distance, at which the force of attraction appears to be interchanged for one of repulsion, might have thrown doubt upon the assumption of a repellent force ; for if there had been two forces, one of attraction and one of repulsion, their ratio to each other would have been the same for all distances. In thinking of magnetic repulsion it should be kept in mind that the process of magnetisation cannot create force, and that there can be no repulsion in a magnetic circuit unless it exists in the particles of which the magnet is composed. If, therefore, there is magnetic repulsion, there must also be gravitational repulsion. But there is certainly no gravitational repulsion distinct and separate from attraction ; and this is obviously the case with mag- netism also. If any one chooses to say that the actual force of attraction between a pound weight and the earth Magnetism. 67 is 20 ounces, but 4 ounces must be deducted for repulsion, there need be no serious controversy between him and another who affirms that there is no repulsion, and that the total force of attraction is 16 ounces. It is well known that terrestrial magnetism has a directive but no convective effect upon a magnetised needle. The needle points to the north, but is not carried in the direction of either the north or south magnetic pole. This is commonly accounted for by saying that the positive and negative poles of the earth repel the similar poles of the needle with the same force as they attract the dissimilar poles; and the length of the needle being a negligible quantity, in respect of the size of the earth, it is not carried towards either pole. Now, this cannot be the correct interpretation of the phenomenon, because, on the same hypothesis, terrestrial magnetism would have no directive effect upon the needle, which is contrary to fact. Let N S be two magnetic poles, and S' N' a magnetised needle placed axially between them. Also, let the distances N S' and S N' be a and h respectively, and I the length of the needle. If attraction and ^'j' ^- -' ^\^ repulsion are equal, the ~ ~ - whole force tending to move the needle in the positive direction, that is, towards S, is p+f— tm ^^^ ^^^ force tending to carry it in the negative direction is -^+ .^ ; therefore, the whole force tending to move the needle is t2+ i-tts!- -§- 7^^-^7^2• When I vanishes, the whole b^ {a + ly' a" (b + lf force vanishes ; that is, there is no convective force. But the directive force vanishes at the same time. For, if the s" ^ "" ^> ■- s' N "^^ J ^'' N' 68 Molecular Forces and Newtonian Laws. needle be placed in the equatorial direction, as S" N", the forces along N S" and N N" coincide when I vanishes, and, since by hypothesis they are equal and opposite, they cancel each other and cannot form a couple. The same rule applies to the forces along S N" and S S" ; therefore, the magnet has no directive effect upon the needle. But terrestrial magnetism has a directive effect upon a mag- netised needle, and therefore the absence of any convective force cannot be due to repulsion, as commonly assumed. If there is a force of attraction between dissimilar poles, and no repulsion between similar poles, the force tending to move the needle S'N' is -I, - \='^- That force vanishes only when a = b; and the motion of the needle is. irrespective of its length, for the magnetic force acts at its extremities only. There is also a directive couple at any position between N and S when the needle is placed obliquely to the axial direction, because the forces acting at opposite ends of the needle form a couple which turns it into the axial direction. That this is the true law of magnetic action can be easily proved by placing needles of various lengths in different positions between the poles of a magnet. The peculiarity of terrestrial magnetism remains to be accounted for. The theory of terrestrial magnetism is at fault. If the earth were a great magnet, as commonly supposed, and the motion of the needle due to the force of attraction between its poles, in the latitude of London there would be a convective force in the northern direction more than twelve times that in the southern. Hereafter an explanation, in accordance with the laws of magnetism, will be given of the fact that terrestrial magnetism has. no convective effect upon a magnetised needle. Magnetism. 69 If the strength of a magnet is F when the poles are in contact, and its length I, the actual strength of the magnet when placed in a non-magnetic medium, is-j^- This force we have denoted by the symbol /. When two magnets, whose forces are F and F' respectively, and their lengths I and I', are situated in a non-magnetic medium at a distance D from each other, the force tending to bring them together is Try— 7-7712- If ^ S'Hd I' be supposed to vanish — that is, the length of the magnets to become a negligible quantity in respect of the distance between them — the force bringing them together is -^- We have also seen that the convective force of a magnet upon a small particle of magnetic matter is the resultant of the two polar forces. When the length of the magnet vanishes the two component forces coincide, and the direction of the resultant is a straight line between the two particles. This is the law of ordinary gravitation, as defined by Newton. The force between any two particles is the product of their masses divided by the square of the distance between them, and the direction of the force is in a straight line between the two particles. We have also seen that a small magnet in the vicinity of another magnet sets itself tangentially to an ellipse of which the poles of the other magnet are the foci. If the small magnet makes an angle x with the tangential direction, its length being I and the force between the two magnets /, the moment of the directive couple isfl sin x. When, therefore, the length of the small magnet vanishes the directive force vanishes. This also is the law of ordinary gravitation. When the length of the atoms or molecules is a negligible quantity in respect of the distance 70 Molecular Forces and Newtonian Laws. between them, there is no directive force ; but when the length of the atoms is an appreciable quantity in respect of the distance, there is a directive couple, as is shown by the crystallisation of the substance when the particles combine in circumstances favourable for the operation of the directive force. It thus appears that the law of ordinary gravitation is the same as that of magnetism when the magnets are of infinitesimal magnitude. In the action of non-magnetic matter there is, of course, no induction. CHAPTER III. ELECTRICITY. 1. Electricity a Force of Attraction. HTHE characteristic of electricity is attraction. When -*- two bodies are electrified so as to form the poles of an electric force, they are attracted towards each other by a much greater force than that of ordinary gravitation. And when contact takes place a spark is produced, which can occur only by the contraction of material particles. Heat may be produced by the contact of unelectrified bodies, but only when they impinge with some degree of mechanical energy, which is expended in producing a state of potential energy among the particles of the body. Heat is then produced by the running down of that potential energy. But when two electrified bodies are brought into contact, without any mechanical energy whatever, heat is produced, thus showing that the particles are already in a state of potential energy, and that the electric force acts upon the contractive side of the heat vibration, and is therefore a force of attraction. Electricity is not to be confounded with the electric spark — they are the direct opposites of each other. Electricity is a force of attraction which brings particles of matter into contact : the electric spark is the kinetic energy produced by the action of the electric force through the available distance, and has a dispellent effect upon the 72 Molecular Forces a'od Newtonian Laws. particles. By the conservation of energy the electric force ceases to act when the spark is produced. The potential is then converted into kinetic energy. This affords a conclusive reply to the theory, adopted by some eminent authorities, that electricity and light are identical. Light is a form of heat, and has always a dispellent effect upon the particles of matter. It is, therefore, the direct opposite of electricity which is a force of attraction. This theory ignores the distinction between potential and kinetic energy, and is therefore at variance with the conservation of energy. The fluid theory, upon which unfortunately our elec- trical terminology is based, confounds matter and force. Electricity, by this theory, is supposed to consist of a fluid, or two fluids, to whose motion all electrical phenomena are due. In observing the spark between the poles of an electric machine, it is difficult to avoid the impression that something passes between them. What the observer actually sees is a small quantity of matter, generally atmospheric air, at a white heat, and the sound by which the spark is accompanied is the agitation of the atmos- phere caused by the collision of the atoms. The foundation of this fluid theory is purely imaginary. We know that a force of attraction exists between all particles of matter, but nothing is known of another kind of matter to which that force is due. Under all varieties of electrical pheno- mena it must be kept in mind that electricity is force and not a particular kind of matter. (See Note 17.) Curiously enough, the converse theory, that matter itself may be resolved into force, has recently found favour among some speculative scientists. The actual relation between force and matter appears to be, that the former is a property of the latter. A substance can never exist Electricity. 73 apart from its property, nor the property apart from the substance, except as mental abstractions. And so, force and matter are never found apart in nature. This new theory appears to have been suggested by the extreme, perhaps unlimited, divisibility of matter. Its advocates are jubilant at the present time over the discovery of radium. But when the nature of that substance has been fully investigated, it will doubtless be found that its particles, like those of all other bodies, whether solid or gaseous, not excepting the ether itself, are regulated by the laws of force and motion, so accurately traced by Newton, and confirmed by the principle of the conserva- tion of energy. Electricity differs very materially from the force of ordinary gravitation. Its intensity is enormously greater. Two electrified bodies are attracted towards each other with a force many times that of ordinary gravitation ; and when the force acts even through an infinitesimal distance, it produces sufiicient energy to drive a mill or to propel a ship. It is also to be observed that after two electrified bodies have been brought into contact, the electric force between them vanishes. When the bodies are again separated after contact, the force of attraction between them is normal only. It is obvious, therefore, that electricity is a form of potential energy which runs down and is converted into heat when the electrified bodies are brought into contact. All potential energy is the product of force into distance: but the distance through which the electric force acts in producing heat is not the distance between the two electrified bodies, because, when thej- are connected by a conductor, the heat produced is the same whether the 74 Molecular Forces and Newtonian Laws. distance is an inch or a mile ; only, in the latter case, part of the heat is found in the conductor. We have seen that a certain motion takes place among the particles of a substance when it is magnetised, and that the motion is reversed when it is demagnetised. Something of the same kind obviously takes place in the case of electricity. When a body is electrified its particles are put into a state of potential energy, and the reverse motion is discharge. The distance through which the electric force acts in producing heat is the distance through which the particles of the substance move. Electrical potential energy is thus the product of an enormous force into an infinitesimal distance. Hence the potential energy cannot be converted into heat until the electrified bodies are in contact. 2. Electricity and Magnetism. Electricity, like magnetism, is polarised force. The positive points of the atoms lie in one direction, and the negative points in the other. Hence electricity, like mag- netism, is complete only in circuit, for then only can there be continuous contact between positive and negative points along the whole line of force. The great strength of magnetic force, compared with ordinary gravitation, is due to the action of the atoms in series along the polarised lines, so that the force is not distributed over a wider area. This, however, is not exactly the cause of the great strength of electric force. In an electric circuit there is motion among the particles, which are alternately in a state of potential and of kinetic energy, The force is polarised, for, when the particles of the conductor are put into the state of potential energy, all the positive magnetic points are forced in one direction, and the negative points in the. other, so that the force of Electricity. 75 attraction between them, to which the name electricity is given, is polarised. The great strength of electric force is thus due to attraction between polarised particles, with a distance between them through which the force can act. When the particles of a conductor are polarised, the sum of all the positive magnetic points is called the positive pole of the force, and the sum of all the negative points is called the negative pole. If the lines of force between the poles lie through a conductor, motion is transmitted from particle to particle through the whole circuit, and the force is discharged. If the lines of force lie through a non-conductor, discharge cannot take place, because the substance does not possess molecular mobility, and resists motion. But the electric force acts through the substance, because force acts by contiguous particles, and is never resisted. When contact is made by means of a conductor motion takes place along that line, and the force is discharged. The only difference between a discharge of static electricity and an electric current is, that the former is a single discharge, while the latter consists of many discharges in rapid succession. Every line of force has a positive and a negative pole, because force exists only between dissimilar points. In electricity the force is polarised, so that all the lines of force have their positive poles in one direction, and all their negative poles in the other. And this is all that is meant by positive and negative electricity. There are not two kinds of electricity, but only electric force between two dissimilar poles. Our terminology in this respect is defective. We have several names to denote force, but no names for the positive and negative elements necessary to constitute force. A force, /, is the product of two 76 Molecular Forces and Newtonian Laws. elements, + \/^. We have several terms for the rational quantity /, but none for the imaginary quantities or surds. For this reason it is sometimes difficult to be quite accurate in expression. When, therefore, words are used implying positive or negative force, it must always be understood that only the positive or negative element, or pole, of the force is meant. Since the peculiar force of magnetism is due to the action of the particles in series, the two poles of a magnetic force are in the same substance. There cannot be a positive magnetic pole in one substance and the corresponding negative pole in another. In an electric circuit there is communication of motion from particle to particle between the two poles. There can, therefore, be no static electricity unless the poles are in different conductors insulated from one another. And since the motion proceeds from particle to particle between the two poles, in the case of static electricity the force lies between the particles on the surfaces only of the two oppositely electrified bodies forming the poles of the force. Between two electrified bodies there is a very strong force of attraction tending to bring them into contact ; but that force through a non-conductor is mechanical only, the same as gravitational or magnetic force. A certain amount of work is necessary to remove the electrified bodies to a distance from one another, but that work adds nothing to the electrical charge. The same amount of work is obtained by again allowing the bodies to move towards each other, but the charge is not thereby diminished. That force between the electrified bodies acts through a non-conductor according to the law of inverse squares, but the electric charge remains unchanged until contact is established between the two bodies. Electricity. 7T There is also a striking resemblance between electric and magnetic attraction, but in their action they are quite different. Static electrical force electrifies a conductor, but does not magnetise a paramagnetic : magnetic force magnetises a paramagnetic, but does not electrify a conductor. A piece of iron is affected by both, but it is electrified in the one case and magnetised in the other. It is also to be observed that the electric charge is partly run down by electrifying the conductor, but the magnetic force undergoes no change in magnetising the para- magnetic. The reason is, that magnetism is a force inherent in the particles of the magnet ; electricity is a state of potential energy, and is run down by doing work. 3. Electricity and Work. The electric and magnetic circuits differ very materially in respect of work. In a magnetic circuit there is no- motion, and no work is required to maintain it after the substance has been magnetised. In an electric circuit the particles of the conductor are in a state of motion, and a constant expenditure of work is necessary to maintain that motion. A certain amount of work is required to put the particles of an iron bar into the magnetic state, and the same work is restored in the form of heat when the particles again fall into the unmagnetised- state ; but no work is required to maintain the magnetic circuit, which is merely the force inherent in the particles of the substance. In the case of soft iron the particles need to be kept in the magnetised state, but no work is required : mere pressure is sufficient. In the case of hard steel even pressure is not necessary. The particles retain the magnetised state of their own accord. 78 Molecular Forces and Newtonian Laws. An electric circuit is a combination of work and force. Not only are the particles of the conductor polarised, but they are alternately in a state of potential and kinetic energy. To produce the first requires work, and by the second the work is again converted into heat. An electric circuit thus consists of a succession of interchanges of potential and kinetic energy. The term electricity is properly applicable to the first of these only. The substance is electrified when its particles are put into the state of potential energy, and the electricity has vanished when heat is again produced. Interchanges of potential and kinetic energy may be maintained by raising any heavy body, such as water, from the earth and again allowing it to fall. The heat produced by the fall is the exact equivalent of the work expended in raising it, except for loss by friction. The same action, in a molecular form, is what goes on in an electric circuit. Instead of the work being expended in raising a heavy body against the force of gravitation, it is expended against the force of attraction between the particles of the conductor, so as to put them into a state of potential «nergy, and the heat produced by the reverse action of the particles is the exact equivalent of the work done, except for friction, or resistance, as it is commonly called in electrical operations. There is a striking resemblance between an electric current and a heat wave. A wave of ether consists of a succession of expansions and contractions, and consequently of interchanges of potential and kinetic energy. The wave motion of the electric current is the same, but instead of that very subtle element the ether, and the feeble contractive force between its particles, the substance of the electric wave consists of the particles of the conductor. Electricity. 79 and the contractive force is the polarised attraction between them. The heat wave and the electric current are also alike in this respect, that both transmit energy. The interchanges of potential and kinetic energy in an electric current proceed in regular succession round the whole circuit, because the positive element of the force is at one end and the negative element at the other. The rate at which the succession proceeds is the velocity of the current; and since every interchange of potential into kinetic energy produces heat, there is a succession of heat waves in the same direction and with the same velocity as the current. It will be shown hereafter that the direction in which these waves move is from the positive towards the negative pole of the circuit. These waves are of very great importance because of their magnetising power. They are commonly called " electric waves," but they are merely heat waves, produced in the same way as heat waves from the fall of a heavy body, or the consumption of fuel. The work of an engine employed to generate an electric current is converted into work in a molecular form. The current is readily converted into light or heat by passing- it through certain substances. When it is desired to re-convert the current into mechanical work, the poles of the force must be connected with two surfaces of consider- able area, so that a great number of molecular forces may act in parallel between them. The principle is the same as that of a steam engine. But instead of being forced apart by a power of expansion, as in the cylinder of the steam engine, the surfaces are forced towards each other by a power of contraction. This is the principle of the electro-motor. The heat generated in the conductor is so much energy lost. 80 Molecular Forces and Newtonian Laws. 4. How Electricity is Generated. The polarisation required to produce an electric current is generally obtained, in artificial appliances, by means of a magnet. To Faraday we owe the important discover}' that an electric current is generated in a conductor, such as a copper wire, when it is passed through the lines of force between the poles of a magnet. The same result follows, of course, when the conductor is stationary and the lines of force move. All that is required to produce a current is relative motion between them, provided always that the motion of the conductor is transverse to the lines of force. Motion along the lines of force does not produce a current. To express more definitely the relation between the motion of the conductor and the direction of the current, let us suppose the observer has before him a copper wire in the vertical direction, and that his right hand represents the positive, and his left hand the negative, pole of the magnet. If he thrusts his hands forward so that the lines of force pass through the wire in that direction, an electric current passes downwards in the wire. But if either the motion of his hands or the relative position of the poles be reversed, the current passes upwards. This rule never varies. The direction of an electric current is supposed to be from the positive towards the negative pole of the force. This is what we have also called the positive direction of a magnetic circuit. This rule is commonly said to be conventional only, but there is a reason for it in nature. To whatever physical cause it is due, the succession of interchanges between potential and kinetic energy in an electric circuit proceeds in that direction. Electricity. 81 Lines of magnetic force offer resistance to the passage of a conductor through them. This shows that work of some kind is done by the movement of the conductor. The negative points of the atoms are necessarily attracted towards the positive pole of the magnet, and the positive points towards the negative pole. These points are held in a certain position by the natural force of attraction which exists between all particles, and when the conductor moves, work is done against that force. The effect of that work is to put the particles of the conductor into a state of polarised potential energy. When the conductor does not move, no work is done, and there is no electrification. So long as the conductor moves in the same direction through the lines of force, the electric current is in the same direction, but if the direction in which the conductor moves, or the relative position of the magnetic poles be reversed, the direction of the current is reversed also. The work done in moving the conductor through the magnetic lines of force is expended against the force of attraction between the particles of the conductor. No change whatever takes place in the lines of magnetic force, which are merely the implement by means of which work is done against the molecular forces — the grappling- hook, so to speak, by means of which we get hold of the magnetic points of the atoms, and are able to move them in a certain direction. But work done against the force of attraction necessarily produces potential energy, and the alternate production and running down to heat of that potential energy is the characteristic action of an electric current. The effect of passing a conductor through magnetic lines of force, or the work of a dynamo, which is a machine for that purpose, is to produce a state of potential energy F 82 Molecular Forces and Newtonian Laws. among the particles of the conductor. All potential energy is the product of force into distance. But by distance in this case is to be understood distance between the magnetic points of the monads, and not between the monads or particles themselves. When any two particles are put into this position there is a force tending to bring the dissimilar points into contact; and when all the particles of a substance are put into this state, all the positive poles being in one direction, and all the negative poles in the other, the force is said to be polarised, and is very great. The product of this force into the distance between the magnetic points of the monads is the potential energy of the electrical charge. When a conductor, in the form of a circuit, is electrified by a machine, the positive element of the force is at one extremity of the circuit and the negative element at the other. Between these the force acts through the con- tiguous particles. But the particles, being all movable, the force and motion between any two contiguous particles are the same as if contact were made between the particles at the extremities. Any loss of power caused by the resistance of the conductor affects every part of the circuit alike. If a bad conductor be inserted at any point in the circuit the heat produced is the same. This accounts for the transmission of energy to a great distance, and with great rapidity, by means of an electric current. If the circuit be 2,000 miles in length, the same work can be done at its remotest point — 1,000 miles — as at any point close to the machine. There is more loss of power by resistance in a long circuit than a short one, but the available work is the same at any point in the same circuit If the common theory were correct, that an electric current proceeds from higher to lower potential, more Electricity. 83 work, or heat, would be available at one part of the circuit than another. But this is not the case. The power available for an electric car at the remotest part of the circuit is the same as for one close to the electric station. The error has arisen from thinking of electricity as some- thing that moves, instead of a force that causes motion. And since there is no dispersion of force in a polarised conductor, the power is the same at every point in the circuit. (See Note 18.) 5. Different Ways of Generating Electricity. Electricity can be generated in various ways, but it is probable that they may all be reduced to the same principle. When a stick of sulphur is broken the surfaces of the fracture are electrified. Like some other brittle sub- stances, and many crystals, the particles of sulphur appear to be so arranged that when the substance is fractured a greater proportion of the positive magnetic points is presented on one side of the fracture, and of the negative points on the other. Between these, polarised lines are formed, and the motion of these lines in the process of breaking the substance appears to be the cause of electri- fication. In the same way may be explained the old experiments of producing electricity by rubbing a glass rod, or a stick of sealing-wax, with silk, cat's fur, &c. The proportion of positive and negative points on the surfaces of these sub- stances appears to be different, so that polarised lines of force are formed by their contact, and the motion of these lines in the process of rubbing generates electricity. The surfaces of almost any two substances when rubbed against each other produce electrification, but the same effect is 84 Molecular Forces and Newtonian Laws. not produced when two surfaces of the same substance are rubbed together, presumably because the proportion of positive and negative points is the same in both, so that no polarisation takes place, the lines of force lying in equal numbers in both directions. In the above cases no magnet is used, so that any peculiar property of magnetism is eliminated from the investigation of the origin of electricity. Only polar- isation and energy appear to be necessary, and magnetism is but a particular form of polarisation. Electricity is also generated when the molecules of some substances are broken up into their constituent elements. Of this an instance is afforded by the galvanic battery. Hence the opinion of Faraday, that electricity is in some way connected with chemical affinity ; and there is, at least, a close analogy between electrification and the process by which molecules are formed out of primary elements. Apparently polarised lines are formed between some of these elements in their nascent state, and these together with the motion produced in the battery may account for the electric current. The facts of thermo-electricity can be readily accounted for in the same way. When the junction of two metals is heated a current of electricity passes in one direction or the other according to the nature of the metals. But this does not occur when only one metal is used, unless it contains some impurity. Comparing this with the facts of " frictional electricity," it may be inferred that polarised lines are formed by the junction of the two metals. These lines are necessarily set in motion by heat, and thus the essential elements of electrification are present. Atmos- pheric electricity, as will be seen hereafter, affords a striking illustration of the same law. Electricity. 85 It thus appears very probable that electricity may in all cases be traced bo the performance of work by means of polarised lines of force. 6. Conductors and Non-Conductors. Substances are divided electrically into conductors and non-conductors, or insulators. These terms denote different degrees of molecular mobility. The particles of an electrified body are in a state of potential energy, and can be put into that state only by motion of some kind. That motion is produced by the action of polarised lines of force. Discharge is the running down of the potential energy, and is produced by the force of attraction among the particles. All substances, therefore, are more or less readily electrified according to the mobility of their particles by these molecular forces. Bodies whose particles are incapable of beingmoved by polarised lines of force cannot be electrified. We have seen that conduction of heat also depends upon molecular mobility. Hence the general rule, that good conductors of heat are good conductors of electricity. Nearly all substances can be electrified, more or less, by the process of friction. Some very decided non-conductors such as glass, sealing-wax, and vulcanite, can be quite readily electrified in this way. The reason seems to be that in the frictional process the polarised lines lie between the particles of the two substances which are in contact, whereas, in passing a non-conductor through lines of force between the poles of a magnet the distance between the magnetic points is at least the whole thickness of the substance. The polarising force is, therefore, much greater by the frictional process than by the other, and serves to electrify the particles of bodies having a very low degree of molecular mobility. 86 Molecular Forces and Newtonian Laws. When the surface of a non-conductor is electrified by friction, it retains the electrification much more tenaciously than a conductor, because there is no transmission of the potential energy among its particles. Every electrified particle is in itself the insulated pole of a small electric force, and discharge can take place only by contact with the opposite pole of the force. This can be shown by presenting the knuckle to an electrified glass rod. A small spark is produced, but only the electricity at that part of the glass rod is converted into heat, because the same thing occurs when the knuckle is presented to another part of the electrified rod. The degree in which the particles of any substance are moved by the action of polarised lines of force is called the conductivity of that substance. Resistance is the opposite of conductivity. A perfect conductor has no resistance, and a perfect insulator has no conductivity. The measures of these two properties are therefore reciprocal numbers. Their product is always unity. If R be the resistance of any substance, its conductivity is -o-- It is probable that no substance is a perfect insulator. The nearest known approximation to it is dry air. The nearest approach to a perfect conductor is pure silver. The difference between these two substances is practically infinite. The conductivity of silver is millions of millions of times greater than that of dry air. Other substances lie between these extremes, but there is no line of demarcation. Substances are called conductors which possess a high degree of conductivity, and substances which have a high degree of resistance are called non- conductors or insulators. The term resistance is not applicable to magnetism, because it is a form of force which acts by contiguous Electricity. 87 particles and is never resisted. This rule applies also to electricity. The force between two electrified bodies acts through all substances, but is greater or less along any particular line, according to the degree of polarisation. An electric current, however, implies motion, and the term resistance is applicable to conductors, which offer more or less resistance to the motion of their particles. An electric current therefore acts along the line of least resistance. When two electric poles are connected by two or more conductors, the current along each conductor is inversely as the resistance. Since the resistance of a uniform conductor is in proportion to its length, it is obvious that the current through any number of conductors may be equalised by varying their lengths. The total conduc- tivity between two electric poles is the sum of the conductivities of all the conductors. For this reason an electric current through the earth is generally greater than through a wire, because the conductivity is practi- cally unlimited. 7. Electric Force through a Non- Conductor. When two electrified bodies are insulated from each other by means of a non-conductor, the lines of force pass through the substance, which, on that account, has been termed dielectric. But, since the dielectric does not possess molecular mobility, no discharge can take place until either contact is made by means of a conductor, or a rupture of the dielectric occurs by reason of the strain upon it. A good illustration of the action of electric force through a dielectric is afforded by the passing of a thundercloud over the earth, with a stratum of dry air between them, the earth and the cloud being the two poles of the force. Although there is electric force 88 Molecular Forces and Newtonian Laws. between the earth and the cloud, no discharge takes place until contact is established by some means, such as a lightning conductor or a rupture of the dielectric, when a flash of lightning, accompanied by a peal of thunder, is the result. It has been abundantly proved by experiment that electric force acts through the atmosphere according to the law of inverse squares. But the total force between two electrified bodies, at any distance from each other, must be the same as at the point of contact, only distributed over a wider area because force can neither be increased nor diminished. It thus appears that electric force radiates through space by the same law as gravita- tional force. (See Note 19.) When the distance between two electric poles is so small that it may be disregarded, the force radiates equally in all directions through the dielectric, so that the equi- potential areas are the surfaces of a series of concentric spheres of which the electric poles are the centre. The total force at the surface of every sphere is the same, and its intensity is inversely as the area. The direction of the force at any point is in a straight line towards the centre of the sphere. This is the law of gravitation, in which all the monads are of infinitesimal magnitude. When there is an appreciable distance between the two poles, the equipotential areas are the surfaces of a series of ellipsoids of which the two poles are the common foci. At any point in the surface of one of these ellipsoids the force is inversely as the area, and its direction is the line of resultant of the two polar forces. This is also the law of gravitation when the monads are so near each. other that their magnitude is an appreciable quantity in respect of the distance between them. (See Note 20.) Electricity. 89 Whatever the form of the equipotential surfaces the direction in which the force radiates through space is always normal to these surfaces. This law applies also to the electrified bodies themselves. Whatever their form, the radiating lines of force are always normal to the surface. For, if this were not so, a current would be set up in the electrified body in the direction of the force through the dielectric. The force may be much greater at one part of the electrified body than another, but it is always normal to the surface. The radiation of force from the surface of an electrified body explains the fact that when an unelectrified conductor is brought into contact with an electrified body the force becomes equally distributed over both. Let A be an 90 Molecular Forces and Newtonian Laws. electrified body, and B an unelectrified conductor. The lines of force from A radiate through the dielectric, as shown in the figure. When B is connected with A, the lines of force radiate from the whole surface as if they formed a single electrified body. The reason is, that the conductor offers no resistance to electric action, which passes through it to the surface, where it is arrested by the dielectric. From this law it can be shown that the electric force between two electrified bodies is independent of their size, because any number of conductors may be connected with either of the poles without altering the force. If two small balls are electrified so as to form the poles of an electric force, and one of them be connected with the earth, the force between the other ball and the earth is the same as between the two balls. The earth, being a good conductor, and very large, becomes readily connected with any electrified body, and forms along with it one of the poles of the electric force. Thus, in experimenting with any electrified body, the other pole of the force is generally the earth. This may be illustrated by the homely experiment of electrifying a piece of well-dried brown paper by rubbing it briskly on one's trousers. The paper, when placed against the wall, adheres to it, thus showing that the other pole of the force has found its way to the earth, and that the wall is a stronger field of force than the atmosphere. This contact with the earth of nearly all conductors, unless specially insulated from it, seems to have given the impression that the earth is an endless source of electricity. But the earth differs in no respect from other conductors. It can be electrified only by contact with some other electrified body ; and when it forms one of the poles of an Electricity. 91 electric force, the other pole being insulated from it, the force is always greatest between their nearest points — -that is, between the insulated pole and the nearest conductor connected with the earth. It might be supposed that when so many electric forces have one of their poles in the earth, and the other in some insulated body, the poles in the earth would get mixed up, and interfere with one another. Nature makes no such confusion. Any number of electric poles, partly positive and partly negative, may co-exist in the earth without any discharge between them, so long as the opposite poles remain insulated ; and the discharge of any one force does not interfere with any of the rest. This can be shown by means of two Leyden jars. Let the inner coating of the one be charged positively, and of the other negatively; their outer coatings, though oppositely charged, may be connected with each other and both of them with the earth, without any discharge, and either of them may be sejjarately discharged without affecting the other. From this may be inferred the important conclusion that oppositely electrified bodies are neutral to each other, unless they form opposite poles of the same force. Two oppositely charged clouds are neutral to each other if the one has its opposite pole in another cloud, and the other its opposite pole in the earth. 8. Electrical "Induction." When a conductor is placed between the poles of an electric force and insulated from both, the lines of force pass through it and it becomes electrified. Let N and S be two electric poles, and N' S', a small bar of copper suspended between them. That the bar is electrified is shown by the separation of the pithballs attached to it by 92 Molecular Forces and Newtonian Laws. a conductive fibre. When the bar is equidistant from the electric poles, it hangs perpendicularly, and the neutral point is at its centre, as shown by the pithballs hanging in contact at that point. If the bar is not equidistant y//////////////////////////^^^ 'kd ^ T N' 0=* from the electric poles, it moves towards the nearer pole, and the neutral point also moves towards that end of the bar. If the pole S be removed and connected with the earth, the only difference is, that the bar moves a little nearer N, and the neutral point a little nearer S'. This is the condition under which the operation is generally per- formed, the operator giving his attention to one electrified body only. In these circumstances the earth is generally the other pole of the electric force. The explanation commonly given of the phenomenon is, that the electrified body N, attracts the negative electricity of the copper bar and repels its positive electricity. The action of the other pole of the force is entirely overlooked, and the bar is said to be electrified by " induction " by the electrified body N. But there can be no electric force at all, except between two poles, and why should the force be called repulsion when the bar moves towards the one pole, and attraction when it moves towards the other ? This applies also to the neutral point of the bar. Its particles are more Electricity. 93 strongly attracted in the one direction or the other accord- ing to whichever pole is the nearer. The hypothesis of a force of repulsion is quite unnecessary to account for the phenomenon. The electric force is greater than gravita- tion, but the same law is applicable to both. The direction and movement of a conductor between two electric poles are the same as those of a magnetic substance between two magnetic poles. The direction in which the electrified bar moves is the line of the resultant of the two polar forces, and the position of the bar is tangential to an ellipse of which the electrical poles are the foci. If the operations are performed in air, the magnetic field is much stronger than the electric field ; because the atmosphere is a magnetic element, whereas it is almost a perfect insulator of electricity. When the conductor, electrified by induction, touches either pole, there is a discharge, the amount of which is directly as the size of the conductor and inversely as the distance between the poles. The nearer the poles are to each other the greater the intensity of the lines of force, and the greater the surface of the conductor the greater the niimber of lines intercepted by it. The distance between the poles is also diminished, more or less, by the conductor, by its full length when it lies in an even line between them. A certain amount of work is done by the electric charge in polarising the conductor, and the charge is run down to that extent, the equivalent of the heat produced, when the conductor touches either pole. The particles of the con- ductor are put into the electrified state by the lines of force, but the reverse motion cannot take place till contact is made with one of the poles. If the force were to act 94 Molecular Forces and Newtonian Laws. and cease alternately, action would go on within the conductor, and after a time the whole charge would be expended in heating it. When tension is applied to a straight wire, no work is done ; but if part of the wire is converted into a spiral, and the tension alternately acts and ceases, work is expended in heating the spiral of the wire. In the same way the electrical charge would be converted into heat within the conductor. The particles would be alternately polarised and depolarised, the former motion requiring work, and the latter producing heat. Those cases in which a conductor is electrified without contact with any electrified body may be very appro- priately ascribed to induction; but the term is often applied to what is really the opposite pole of the force. Especially is this the case when the earth forms the missing pole. When the electrified body is brought near any good conductor connected with the earth, an opposite electrification is found in that conductor, and it is ascribed to induction ; but it is only the co-ordinate element of the same force, equal to it, and produced at the same time. So also, when a Leyden jar is charged by means of a conductor connected with the earth, the current is commonly said to be obtained by induction. But there is no induction in the case. The current passes through the earth the same as it might pass through any other conductor. Owing to its great size the earth gathers up all the lines of force, and often produces better results than a direct wire from the battery to the jar; but this is not induction. 9. No Electrical Repulsion. All cases of alleged repulsion belong to static electricity — that is to say, they are connected with phenomena in which the force acts through a dielectric. No irepulsion is Electricity. 95 ever alleged in connection with kinetic electricity, in which the electrified particles are in contact with one another. All supposed repulsion is accordingly explained by the radiation of electric force through a dielectric. Let A B A' B' be an electrified metallic sphere, the centre of which is N, the other pole of the force being S. Join S N by a line cutting the surface of the sphere in A, and produce the line to A'. Also draw a diameter, B B', at right angles to A A'. The figure is on a plane, but if it be supposed to revolve about the axis, S A', it describes a figure of three dimensions, which represents the actual state of the case. Since the lines of force between the two electric poles are normal to the surface of the sphere, they may all be resolved into three pairs of opposite forces — -two pairs along the diameters, A A' and B B', as shown by the small arrows, and another pair along a diameter at right angles to these and perpendicular to the paper, which cannot be shown on the figure but may be called G C. By Eu. iii. 8, the force A is much greater than the force A', and their difference is the force which tends to bring the two electrified bodies into contact. The forces BB', as also the forces C C, are equal and opposite, and do not move the sphere, but produce a slight strain upon the cohesion of the substance. If we now suppose the sphere to be divided into two hemispheres by a plane at right angles to the line of any 96 Molecular Forces and Newtonian Laws. of these pairs of opposite forces, the hemispheres are carried in opposite directions by these two forces. There is no electric force between the particles of an electrified body ; for the force exists only between the opposite poles. The only force, therefore, which holds the two hemispheres together is ordinary gravitation ; and since electric force is much greater than gravitation, the two hemispheres are carried in opposite directions. This is the phenomenon which has been ascribed to repulsion, but it is manifestly due to attraction in opposite directions. When any conductor is attracted by induction to one of the poles of an electric force, it becomes similarly electri- fied. The two bodies then act in the same way as the two hemispheres above described. When a small piece of straw, or a scrap of paper is attracted to an electrified body, the lines of force radiate from both, the same as if they formed a single body. But they are held together only by the force of ordinary gravitation, and are therefore forced apart by electrical attraction. For the same reason a pithball starts off from an electrified body after touching it. In this way every case of apparent repulsion is accounted for by radiating lines of force acting upon two similarly electrified bodies in contact, and between which there is no cohesion. In all such cases the motion of the electrified particle is towards the opposite pole of the electric force ; but the motion is not generally in a straight line, because it always begins at right angles to the one surface and ends at right angles to the other. When the particle touches the opposite pole the charge is reversed, and it moves towards the same pole once more, but generally in a straight line, because that is the line of greatest force. The particle continues to vibrate between the two poles Electricity. 97 till the whole force is discharged by the alternate contacts. This is the principle of the electric pendulum, and is also illustrated by the interesting experiment known as Volta's theory of hail. In all these cases the only force is attraction ; there is no repulsion. When two similarly electrified bodies are in contact, their adjacent sides are screened by each other. The lines of force radiate from their other sides only. But when the two bodies move away from each other, the screened portions gradually diminish till the lines of force radiate from the whole surface of both. The amount of the separating force, or apparent repulsion, is therefore in proportion- to the screened area. If that area be x when the two bodies are in contact, then at any distance d, the screened area is the space occupied by x on the surface of a sphere of which the other body is the centre. At the distance d, therefore, the screened area is-jrj thaA, is to say, the apparent repulsion is inversely as the square of the distance between the two similarly electrified bodies. Coulomb was quite correct in his measurement of the force, although he was mistaken as to its nature. He used for the purpose a torsion balance, which consists of a light bar of non-conductive material with a conductive ball attached to one end, and supported at its centre of gravity by a very fine wire. When the ball is touched by an electrified ball of similar size, they are separated by a certain force which is measured by the torsion of the wire. Coulomb found that force to vary inversely as the square of the distance between the two balls. And he obviously measured the separating force only; because the opposite pole of the force was the earth, and the 98 Molecular Forces and Newtonian Laws. distance from that pole could not be appreciably affected by the motion of the ball, unless some conductor connected with the earth was close by, which was not likely to be the case. Since the time of Coulomb it has been accepted as a well-established law that similarly electrified bodies are repelled by a force inversely as the square of the distance between them. For " repelled " it is only necessary to substitute " separated." This little change reconciles the science of electricity with the Newtonian law of universal gravitation. CHAPTEE IV. ELECTRICAL PHENOMENA. 1. Electricity at the Surface only. rpHE view of electricity which has just been given affords ■^ a complete explanation of all electrical phenomena. Of these, a few examples are given in this chapter. Electricity is commonly said to reside on the surface only of an electrified conductor. Properly speaking, electricity does not reside in a body at all : it is a force of attraction between two bodies. But the electric force exists between the particles at the surface only, and does not extend through the substance of the body. Any hollow metallic shell has the same electrical capacity as a solid body of the same form and size. If a solid metallic sphere be fitted with a thin cover of the same material, consisting of two hemispheres, and the whole electrified, when the cover is very carefully removed so that its edges do not touch the surface of the sphere, the whole charge is found in the cover. It has also been shown that there are no traces of electricity in the hollow of an electrified conductor. These facts are somewhat perplexing at first sight, and created no little astonishment when first discovered. But the reason is quite obvious when the action of electric force through a non-conductor is taken into account. The 100 Molecular Forces and Newtonian Laws. lines of force radiate from the surface of the conductor, but the motion of the particles is arrested by the dielectric, so that the whole force lies between the particles on the surface and the other pole of the force. No force through the dielectric can act between the particles within the conductor, because in that case there would be a current towards the surface, which implies motion. In magnetism there is no motion, and the magnetic force acts between particle and particle throughout the whole length of the magnet ; but, from the nature of electricity, the force can exist only between the particles in the surfaces of the two electrified bodies. This affords a complete explanation of Faraday's celebrated ice-pail experiment. Let A B A' be a section of a common metallic ice-pail, strongly electrified, the earth being the opposite pole of the force, as is usual in all such cases. The lines of force radiate from the ice-pail in all directions, as shown by the small lines in the figure. The whole electric force, therefore, acts upon the outer surface "~^|,:^'jfeigB wAt8r^fcgJ^^B^ '! i; ^j ^§?fe ' ;^t' : i^r^^^^ of the ice-pail, and no lines of force pass through the hollow space within. It might be supposed that some lines of force would pass from the interior surface, at B, Electrical Phenomena. 101 towards the mouth of the ice-pail between A and A', but the lines of force in that direction act at A A', the rim of the ice-pail, in accordance with the power of points, as will be explained hereafter. If a conductor, C, connected with the earth, were introduced within the ice-pail, there would be lines of force between it and the interior surface of the ice-pail, and, if connection were made, the whole force would be discharged. Since electric force acts at the surface only of a con- ductor, it is obvious that in order to estimate the amount of force between two electrified bodies according to the law of inverse squares, the distance between them must not be measured from their centres of gravity, as in the case of gravitational force, but between their nearest points. An electrified conductor, whatever its size, is only a point in respect of electric force. Hence, also, the discharge of the whole force between two electrified bodies when contact is made at a single point. Whatever the size of the conductor, the discharge is practically instantaneous. This point is interesting, inasmuch as it accounts for the intense heat of the electric spark. In all other cases, heat is produced by the contact of atom with atom. The heat of a common fire is due to the contact of individual atoms of carbon and oxygen in their nascent state. In like manner, the explosion of gases consists of the simultaneous contact of innumerable atoms ; but still the contact is between atom and atom. In the case of electricity, the force of attraction between innumerable atoms is converted into heat at a single point. In a lightning discharge, for instance, the whole electric force between some acres, perhaps, of electrified cloud, and as many acres of the earth's surface, is con- verted into heat at the point of contact. Although the 102 Molecular Forces and Newtonian Laws. volume of heat may be small compared with that produced in other ways, no heat from any other source can be com- pared in respect of intensity with that of the electric spark. The existence of electrification at the surface only is peculiar to static 'electricity. When a current passes through a conductor, the force acts between all particles of the substance alike. Hence the capacity of an electric cable is in proportion to its sectional area, not its circum- ference. It has been supposed that the current passes along an insulated cable close to the insulating substance ; but, if so, it is due to the influence of the other pole of the force. If the insulation were weak that influence would produce condensation, and the cable would cease working. 2. Electrical Condensation. The process by which a powerful force is established between two conductors is called electrical condensation. The principle is of great practical importance in electrical engineering, and is of considerable interest as illustrating the exact parallel between electricity and gravitation. The appliance required to produce condensation consists of two conductors of considerable surface placed near each other, with a non-conductor between them. Two sheets of tinfoil attached to the opposite sides of a pane of glass answer the purpose. One of these is commonly connected directly with the positive pole of the electrical machine, and is called the collecting "plate ; the other is generally connected through the earth with the negative pole of the machine, and is called the condensing plate. These terms are based upon the old fluid theory ; but the two plates are merely two conductors of considerable surface, connected with the poles of the machine, and separated by a thin insulator of some kind. The most convenient Electrical Phenomena. 103 condenser is the common Leyden jar, the inner coating of which may be called the collecting plate, and the outer coating the condensing plate. When the machine is worked, a strong electric force is established between the two coatings of the jar, and remains after the jar is disconnected from the machine. The essential condition of success in this operation is, that the insulation between the two plates be less than that between the poles of the machine by any other channel ; for otherwise the force acts along that line, and not between the two plates. The case is simply one of greater attraction in the one direction or the other. When a chain is passed over a pulley, if only a small portion of the chain is passed over, it runs back as soon as the work ceases ; but if a sufficient length of chain is passed over the pulley to counterbalance the suspended portion on the other side, every link remains on that side after the work has ceased. This, also, is a case of greater attraction in the one direction or the other. The law of gravitation is also the law of electricity. The potential of the condensed force is also regulated by the same law as gravitation. When water having a certain head is conducted into a closed vessel by means of a pipe, the pressure in the vessel may be increased till it is equal to that of water from the head, but no more. The electrical charge may, in like manner, be increased till the potential is equal to that between the poles of the machine, but can never exceed it. In this respect, also, the law of gravitation is the law of electricity. Since electricity resides on the surface only of a con- ductor, the amount of the charge, after it has reached the potential of the machine, can be increased only by increas- ing the surfaces of the two conductors. Thus, also, water 104 Molecular Forces and Newtonian Laws. can rise only to its own level, but the power may be increased to any extent by increasing the area of a reservoir at that level. The law of electrical condensation is therefore identical in all respects with the law of gravitation. Electrical condensation often proves very troublesome to the electrical engineer. When a cable is laid underground, or in the ocean, and the return current passes through the earth, all the conditions of electric condensation are present. The cable is the collecting plate, the earth or ocean the condensing plate, and the coating of the cable is the insulator between them. If at any part along the cable the resistance of the coating is less than that of the entire length of the conductor, condensation takes place at that point, and the working of the cable is interrupted. 3. The Cascade. The term cascade is used to denote a special kind of electric battery. It forms a sort of electrical puzzle, and from the explanations of it given by most writers on the sub- ject, its nature appears to have been greatly misunderstood. The arrangement for a cascade consists of a series of Leyden jars insulated from the earth and from one another. '^"'^^f^^m^^^^^^^Wi^i^ Let A, B, C, be the inner coatings of such a series of jars, and A', B', C, their outer coatings. A is connected with the positive pole of the electric machine ; A' is connected Electrical Phenomena. 105 with B, and B' with C ; C is connected with the negative pole of the machine. When the machine has been worked for a time, A, B, C, are all positively electrified, and A', B', C, negatively. The explanation of the charge is quite simple. A and C are directlj- charged from the machine, and that is the only direct force of the battery. A' B and B' C are two insulated conductors placed between the poles of the force, and are charged by induction. The surfaces of these con- ductors being large, and placed very near the poles of the force, the charge is proportionately great. In ordinary circumstances, the charge between the two poles would be run down to the extent of the charge in the two conductors ; but owing to the action of the machine while the inductive process is going on,' the full charge between A and C is maintained without diminution. Discharge of the cascade also follows the rule for insulated conductors. Contact with one or other of the poles is necessary for the discharge of a conductor. Thus , if A A' are connected, there is discharge of the conductor A' B ; but the positive element. A, is still equal to C, because the positive and negative elements of the conductor are equal. The whole positive charge is now in B, and if B B' are connected, the conductor B' C is discharged, and the whole positive element is in C. Connection between C C discharges the whole force, which is not affected by the discharge of the conductors. If A and C had been connected at first, the discharge would have been the same, and the charge of the conductors would have been con- verted into heat in the connecting wires between their positive and negative extremities. The cascade therefore affords a striking illustration of the law of electrical induction. 106 Molecular Forces and Newtonian Laws. 4. The Lightning Conductor. All lines of force between two electrified bodies are normal to both surfaces. If this were not so a current would be set up in the conductor upon whose surface the lines fall obliquely. But the whole force is between the particles at the surfaces of the two bodies, and hence the electrification is not equally distributed over the surface of an electrified conductor. At any point the force is greater or less, according to the number of lines converging at that point. Over the surface of a sphere the electrification is equally distributed, because the same number of lines converge at every point ; but when the other pole of the force is very near, the intensity of the lines is greater on the side next the other pole. An ellipsoid is much more strongly electrified at the ends than along the sides, because, on account of the greater curvature, more lines fall normal to the surface at those parts. In the case of an angular body, such as a pyramid, the number of the lines of force converging upon the edges and angles is immensely greater than the number converging upon the planes, because an angle sub- tends an area which increases with the distance, whereas a plane always subtends the same area, and at a great distance is normal to a very small portion of the surface of the sphere towards which the lines radiate. Let A B C be a small triangular body, and D E F the circumference of a sphere, of which the small triangle is the centre. Draw A D at Electrical Phenomena. 107 right angles to AB, and AE, CF at right angles to A C. The surface D E represents the number of lines of force converging upon the point A, and E F the number converging upon the plane A C. This is the explanation of what is called the power of points, that is, the tendency of discharge to take place through projecting points on the surfaces of electrified bodies. The principle of the lightning conductor is an appli- cation of this law. By means of a mathematical demonstration, it can be shown that the number of lines converging at the point of a conductor is in proportion to the cosine square of half the angle. Let BAG be the point of a lightning conductor projecting from the earth's surface. Bisect the angle BAG by G A and produce to E, and draw A D, A F D E F at right angles to AB, AG respec- tively. At any point E in A E draw g/ i \ ^ JliJ^ at right •'-^■■■■^■'■i:fvK.^!:jS-''-^'^'''- '■^'^■' ''■ ""-^ angles to AE, meeting AD, AF in D and F. The angle BAG sub- tends a circular area of which the diameter is D F, and which varies as the cosine square of A D E. But the angle A D E is equal to the angle BAG, and therefore the number of lines converging at the point of the conductor is in proportion to the cosine square of half the angle. The cosine increases as the angle diminishes, and there- fore the finer the point of the conductor the greater its power in attracting the electricity of the charged cloud. If the angle diminishes almost to the vanishing point, the power of the conductor is at its maximum, because the 108 Molecular Forces and Newtonian Laws. point then subtends the whole hemisphere. If the angle increases to two right angles, it forms a point in the level surface of the earth, and its power vanishes. This shows how small is the force tending to produce discharge at a point on the earth's surface, compared with that at the top of a good lightning conductor. The power of the conductor is also increased by its height above the surface of the earth, in accordance with the law of inverse squares. The effect, however, of both these laws is liable to be modified by the nature of surrounding objects and the conformation of the land- scape. But the general rule applies to all cases, that the higher the conducting rod, and the finer its point, the greater its efficiency as a lightning conductor. 5. Multiplex Telegraphy. Two or more telegraphic messages can be sent simul- taneously along the same wire. It is obvious therefore that as many different currents must pass along the wire at the same time, and that these may be in the same or opposite directions. Apparently a great number of separate currents may thus act along a common telegraphic wire, and in order to utilise them all for conveying messages it is only necessary to take steps to prevent the different currents from acting upon the same needles. This has been attained, as yet, only to a limited extent ; but, in so far as the cables are concerned, many messages might be transmitted simultaneously from different stations. The currents acting along the same cable are quite distinct from one another. The physical law underl3dng this phenomenon is, that electricity, like gravitation, is a force of attraction between particle and particle ; or rather, between the opposite Electrical Phenomena. 109 magnetic points of the same monad. That force acting through the contiguous particles produces contraction. When these particles are polarised, the force along any particular line is very great ; for, as explained by Hertz in the passage quoted in Note 19, the conductor prevents the distribution of the force over a wider area. There is, therefore no electric force between the positive points of one battery and the negative points of another. Hence the electric force between the terminals of one battery is quite distinct from the force between the terminals of another battery, and both act simultaneously along the same cable, if it is of sufficient capacity. It is in this way also, as we have seen, that chemical combination between two or more particles does not affect the gravitation between them and all other bodies, and also that the opposite coatings of two charged Leyden jars have no electrical attraction for one another. There is no electric force between two bodies merely because they have been electrified ; they must be electrified so as to form opposite poles of the same force, and this is not the case with the particles of different batteries. Any number of conductors conveying electric currents may thus have a common segment. If A and B be two batteries, their terminals may be connected with the common conductor C D E, and the cur- rents flow uninter- ruptedly the same as if they were in separate conductors, and that whether the currents pass in the same or opposite directions through the common segment. This is what happens when the terminals of any number of batteries 110 Molecular Forces and Newtonian Laws. are earthed. The earth is the common conductor through which all the currents pass. Owing to its great extent, any number of currents can pass to and fro in it without obstruction. The dimensions of a common cable are limited, and only a limited number of currents can pass through it. Even a single current encounters more resist- ance in a cable than in passing through the earth. A very strong current would obstruct the action of a feeble current, such as is used for telegraphic purposes. The subsidiary currents which are often set up in tele- graph wires during magnetic storms, do not interrupt the currents conveying the messages, but they take possession of the needles and play at cross purposes with the Post Office. If the currents are very strong they may monopolise the wires, arid render impossible the action of the force from the batteries. So long as electricity was associated with matter of some kind, great difficulty was felt about a current passing through the earth or ocean. This difficulty, however, no longer exists when the true nature of electricity is kept in mind. Force acts through all substances, and is never resisted. The gravitational force between two grains of sand on opposite sides of the earth acts through that body. Electric force not only acts in the same way, but, the •earth being a conductor, the force is not dispersed like gravitational force ; and the conductivity of the earth being practically unlimited, the electric force produces molecular motion more powerfully than through a wire of the best conductive material. 6. Wheatstone's Bridge. The contrivance known as Wheatstone's bridge is conveniently used, among other purposes, for measuring Electrical Phenomena. Ill the comparative resistances of two conductors. It depends upon the principle that when an electric current passes through several channels between the poles of a battery, the current through each channel is inversely as the resistance. Let N S be a conductor of uniform resistance, N P a conductor whose resistance is known, and P S a conductor whose resist- P ance it is desired to find in terms of N P. In a» > / 1 "^^ > NS take any *• * ^ point. A, and connect A P by a conductor passing through a small galvanometer, G. When a current passes from the battery there are four channels by which it can pass from N to S, NAS, NPS, NAPS, and NPAS, and the cuiTent along each of these is inversely as the resist- ance. Let the current through N A, A S, N P, and P S be a, b, c, d, respectively, and h the force through the gal- vanometer ; then a ± h = b, and c ±h = d, and therefore r±h ^ d ''^-'■ If a is greater than b, there is force from A to P, and the needle of the galvanometer is deflected to the left ; if a is less than b, there is a force from P to A, and the needle is deflected to the right. But, since N S is a conductor of uniform resistance, the ratio of a to 6 can be varied by moving the point A along N S ; and since either of these currents may be made as near as we please to the whole current along N S, there must be some point between N and S where a = b, and at that point the needle is not deflected, because the current, h, vanishes. If A be that point, then by equation (1) ah a c 112 Molecular Forces and, Newtonian Laws. If we call the resistance of these four sections a', V, d , d', respectively, since the resistances are inversely as the forces, we set — = — ; and therefore d' = —r. But the 'Oaf' a resistance of the conductor, N P, is known, and since N S is a uniform conductor, the resistances of N A, A S are simply as their lengths ; thus, the resistance of P S is found in terms of N P. The accounts usually given of Wheatstone's bridge proceed on the assumption that there is a fall of potential in the current from N to S, and that A is the point where the fall of potential has the same ratio to the whole circuit, N A S, as the fall of potential at P has to the whole circuit, N P S. But the potential of every electric current is the same throughout its entire length, for otherwise the power of the current would steadily diminish from the positive towards the negative pole, which is not the case. The design of the above demonstration is to show that the principle of Wheatstone's bridge is not dependent upon the supposed fall of potential in an electric circuit. The position of the point, A, is determined by the resistances of the different conductors, not by any fall in the potential of the current. 7. Electrical Potential. The term potential is used to denote the intensity of any force. The potential of a jet of steam is the pressure per square inch. The total force of the jet is the product of the area of a cross section by the potential. In the case of water power, the potential is the head, or height, from which the water falls. The quantity of water may be ever so small, its potential depends only upon the height. The Electrical Phenomena. 113 total mechanical value is the product of the quantity of water by the potential. This rule applies also to electricity. A current consists of a certain number of lines of force ; the potential of the current is the intensity of the lines. The volume of the current, or number of the lines of force, is measured in amperes, the potential is measured in volts. The total mechanical value of the current is the product of the number of amperes by the voltage. We have seen that a current of electricity is generated by passing a conductor through a magnetic field of force : it is obvious that the potential of the current must be greater when the strength of the field is greater. The number of lines is the same, but each line is intensified by the increased power of the magnet. Also, if passing the conductor through the field once produces a certain potential, a greater potential must be produced by passing it through the field many times. This is accomplished by winding the conductor upon an armature, so that every convolution of the wire forms an additional passage of the conductor through the field of force. The number of lines is not increased by these convolutions, for they are all con- tinuations of the same conductor, so that they only increase the potential of the same lines. The voltage of a current is quite independent of the thickness of the conductor; but the greater the mass of metal passing through the field of force, the greater the number of lines. Thus, for the same strength of field and number of revolutions, the voltage of the current depends upon the number of convolutions on the armature ; the number of lines, or volume of the current, depends upon the sectional area of the conductor. Subject to the necessary modifications, these rules also apply to the voltaic current. In this case the current is H 114 Molecular Forces and Newtonian Laws. produced by the action of acid upon zinc, and the greater the amount of that action the greater must be the inten- sity of the lines of electric force. But every cell through which the current passes adds a similar amount to the voltage, while the number of lines, or volume of the cur- rent, depends upon the size of the plates. Thus, for the same strength of chemical action, the potential of the current depends upon the number of cells, and its volume upon the size of the plates. The same importance does not attach to potential in connection with static as with current electricity, because in static electricity the number of the lines of force is unlimited. In a current, the lines of force are between the two ends of the conductor only, and the mechanical value of the current depends entirely upon their potential. In static electricity, the number of lines may be increased indefinitely by increasing the size of the electrified bodies forming the poles of the force, and it is only necessary that the product of all the lines of force into their potential be the same. It is not even necessary that the two poles be alike in this respect, for every point in the one may be connected with 100 times the number of points in the other, and each of these lines can have only 1-lOOth part of the potential of a line between two conductors of the same size as the smaller. Still, the total force between the two conductors is the same, and the discharge of all the lines takes place when contact is made. When two bodies are electrified so as to form the poles of an electric force, it would be incorrect to speak of them as having different potentials. Neither of the two bodies can have any potential by itself, because electric force, and, therefore, electrical potential, can exist only between two electrified bodies. The term potential is applicable Electrical Phenomena. 115 only to lines of force, and the positive and negative elements necessary to constitute lines of force are always equal and opposite. Positive and negative points are not different potentials, but only the elements of force. It is generally assumed that there can be no electric current between two bodies unless they have different potentials. The idea seems to be taken from the analogy of water. There is no current between two reservoirs unless they have different heights, or potentials, and it is assumed that this must be a law of electricity also. But, the analogy is incorrectly stated. The force which causes an electric current exists between the two electrified bodies, whereas the force which causes the current of water exists between the two reservoirs and the earth. A correct analogy would be the case of two similarly electrified bodies having their common pole in the earth. When the two similarly electrified bodies are connected by a conductor, their potentials are equalised, just as the potentials of the two reservoirs are equalised by the water rising to a common level. What causes the current of water is a gravitational force between the reservoir and the earth, and it would be meaningless to speak of the earth and reservoir having different potentials. There is a force of attraction between them, not a difference of potential. And this is the case with two electrified bodies, only the force is of greater intensity than gravitation. Potential belongs neither to the one nor the other, but to the force of attraction between them. The fluid theory of electricity is no longer credited. Nearly every writer on the subject expressly repudiates it. Nevertheless, the terminology of the fluid theory is still in use, and the fundamental idea of that theory still dominates all teaching on the subject. Electricity is still 116 Molecular Forces and Newtonian Laws. something distributed in some way over all bodies. The earth is a body whose electricity is in a state of equi- librium, but has an unlimited capacity for either positive or negative electricity. When the junction of two metals is heated, a current of electricity flows in one direction or the other, according to the nature of the metals. This is accounted for by saying that the metals have different potentials. Why, in these circumstances, heat should be necessary is not very apparent, for an electric current in a conductor is said to be due to the difference of potential between its extremities ; and the electro-motive force is said to maintain the current by maintaining this difference of potential. It thus appears that the thing which moves is electricity, and when it is at rest there is no current. This is not merely the language, but the fundamental conception, of the fluid theory, only expressed in less definite terms. Electricity is not a substance which can be moved, but a force which causes motion. An unelec- trified body is not a body whose electricity is in a state of equilibrium, but whose particles have not been put into the state of potential energy, like a bow unbent, or a stone not raised from the ground. A body has no electricity on or about it until its particles have been put into the electrified state by the expenditure of work, and that work is again restored in the form of heat when the particles fall into their former position. 8. The Electrical Engine. An engine is a machine for producing work in some convenient form. But the work done by the engine is necessarily less than the motive power expended, for there is always some loss by friction. The sum by which the motive power must be multiplied in order to give the net Electrical Phenomena. 117 amount of work done by the engine is called the co-efficient of friction, or co-efRcient of resistance in the case of the electrical engine, b'ecause the principal loss is caused by the resistance of the conductor, though there is also some loss by friction in working the machine. Both mean the same thing, viz., that proportion of the motive power which is converted into heat instead of going to produce work. Since the co-efficient of friction is always a sum between unity and zero, it may be conveniently represented by the symbol g-. Thus, if the motive power of an engine is P, and the work done by it W, then -5- = W. In the electrical engine the motive power is commonly called the electro-motive force, and is denoted by the symbol E ; the work done is the current produced, and is commonly denoted by C. Substituting these for P and W in the above formula, it becomes ^g- = C. This is known as Ohm's law. It is of very convenient application to the electrical engine, but it states a principle which is appli- cable to engines of all kinds. In a steam-engine the motive power is a jet of steam, which is a certain force acting through a certain distance in unit time. The work done is generally in the form of a driving-wheel, which is also a force working through a certain distance in unit time, but the product is less than that of the motive power by the amount converted into heat by friction. In the electrical engine the motive power is generally a driving-wheel, and the work done is molecular force acting through an infinitesimal distance with great rapidity, and is called an electric current. The mechanical power of the current is, of course, less than that of the motive power by the amount converted into 118 Molecular Forces and Newtonian Laws. heat by the resistance of the conductor, together with any loss by friction in running the machine. The current is the work done by the engine, and in that form is very convenient for conversion into light or heat ; and also for rapid transmission to a great distance. When it is required for mechanical purposes, the motion has again to be geared down to that of a driving-wheel, by means of an electro-motor. It will be observed that an electric current is a form of work, as much as a jet of steam or the motion of a water- wheel, and can be measured only by some unit of work such as the foot-pound or the grammetre. Electric current is generally measured in amperes at a certain voltage ; but whatever that measure may be, it represents so many foot-pounds, the same as the driving wheel of a steam-engine. The numerical value of a current is commonly defined as "the quantity of electricity that passes in unit time " — a definition which savours unpleasantly of the old fluid theory. Electric power is something far simpler than is commonly supposed. There is no essential difference between it and mechanical energy. Both consist of force acting through distance, but in electricity the force is very great, the distance small, and the action takes place with great rapidity. The product of the force and distance is the mechanical value of the current, which might be measured and sold by the foot-pound or the horse-power, the same as ordinary mechanical power. There would be certain advantages in having a common unit for both. CHAPTER V. ELECTRO-MAGNETISM AND DIAMAGNETISM. 1. Different Modes op Magnetisation. rPHE simplest way of magnetising an iron or steel bar -•- is to bring it into contact with a magnet, when it is magnetised more or less rapidly, according to the nature of the substance. Sofb iron magnetises very rapidly, but loses its magnetism as rapidly when separated from the magnet. Hard steel is more difficult to magnetise, but retains the magnetised state for a great length of time. This process may be called magnetisation by " induction." Whether placed in contact with the poles of the mag;net, or very near them, the iron bar is magnetised by the lines of magnetic force passing through it, in the same way as an insulated conductor is electrified when placed between two electric poles. In this way a steel bar is readily magnetised by drawing along its surface one of the poles of a magnet, the same pole being always drawn in the same direction, or the other pole in the opposite direction. The motion of the magnet is not essential to the magnetisation of the steel bar. The lines of force passing through the bar magnetise it without any motion of the magnet. But the process is greatly facilitated by the movement of the magnet. The same effect is produced by tapping the bar with a small hammer. 120 Molecular Forces and Newtonian Laws. It is on this principle also that substances are magne- tised by the force known as terrestrial magnetism. The atmosphere is a great magnet, and when a magnetic substance remains in that element for a length of time in one position it becomes magnetised by the surrounding element. In this way fire-irons become magnetised, and a steel ship lying in dock for a length of time becomes magnetised in some degree. The greatest strength of terrestrial magnetism is in the direction of the dipping needle, that being the direction in which the atmosphere is polarised. All these cases imply the previous existence of magnetic force. But no substance in its natural state possesses such force. What are called natural magnets are only small pieces of peroxide of iron, a substance which possesses the property of retaining magnetisation for a great length of time, and have obviously been magnetised by terrestrial magnetic force. We have therefore to go a step further, and consider how magnetism can be produced without the aid of any existing magnet — in other words, to investigate the origin of magnetism. Magnetisation by means of electricity brings us a step nearer this consummation. When a wire conveying an electric current is wound round a steel or iron bar, but insulated from it, the bar is immediately magnetised. A magnetic needle is always affected by the proximity of an electric current, and any force which affects a magnetic needle is a magnetising force. The same effect is produced by an electric spark. A powerful electric spark in an underground cellar will magnetise small needles at the roof of the house. A strong electric discharge even produces magnetic effects sufficient to record an intelligible message on the other side of the Atlantic. In order to Electro-Magnetism and Diamagnetism. 121 get at the origin of magnetisation it is obviously of great importance to consider carefully the nature of electro- magnetism. 2. The Hertzian Waves. In all cases of magnetisation by means of an electric current certain waves proceed from the current, by means of which the eifect is produced. Waves of the same nature, but of much greater penetrative power, can be produced by a powerful electric discharge. These are commonly called Hertzian wat)es, from the late Dr. Hertz of Carlsruhe, to whose researches we are chiefly indebted for our knowledge of their nature. These Hertzian waves occupy a very important place in electric and magnetic science. They are commonly described as " electric waves," implying that they convey some kind of electric force. And as they are always accompanied by a magnetising effect upon magnetic substances, their force is sometimes identified with magnetism, which, on that account, has been described as " radiant electricity.'' But electricity and magnetism, like gravitation, consist of lines of force between material points, and do not undulate like radiant heat. The Hertzian waves, however, consist of contractions and expansions of ether the same as heat, and it will now be shown that they are in reality heat waves. The manner in which these waves are generated is contrary to the supposition that they contain any electric force. They proceed from an electric discharge, either at a single point, as in the case of an electric spark, or from a current which may be regarded as a succession of sparks. But an electric discharge in any form is a running down of potential energy to heat, just as the potential energy 122 Molecular Forces and Newtolnian Laws. of a heavy body is converted into heat when it touches the ground. If, therefore, the waves from an electric spark possess any electric force, it must be assumed that some portion of the potential energy of the electric charge is not converted into heat, but is transmitted somehow in the form of radiant electric force ; for, by the conservation of energy, the electric force ceases to exist when the spark is produced. But this is the same thing as if we were to suppose that when a heavy body falls to the ground, some part of its potential energy is not converted into heat, but passes off somehow in the form of radiant gravitation ! The fact that Hertzian waves are never produced by electric force, but by heat only, may be considered as conclusive on this point. When a magnetic substance is placed between the poles of a static electric force, however strong that force may be, no Hertzian waves are produced, and no magnetisation takes place ; but these effects follow immediately the electric force is converted into heat. We have also seen that every electric current consists of interchanges of potential and kinetic energy, and the heat thus produced necessarily causes heat waves to radiate from the conductor. These are the Hertzian waves, and when they cease, the magnetising force ceases. In all cases Hertzian waves are produced by heat only. Hertz showed that these waves correspond in all essential respects with heat waves. They consist of vibrations of ether, like heat waves, and travel with the same velocity; they can also be reflected and refracted the same as heat waves. Having thus arrived in the course of his investigations at the parting of the ways, so to speak, Hertz unfortunately took the wrong turn. Instead of accepting the conclusion that they are heat Electro-Magnetism and Diamagnetism,. 123 waves, and endeavouring to account for their magnetising effects, he assumed the identity of electricity and light, and went on to speak of every fire as a source of electricity, emitting its electric waves into surrounding space, and the human eye, which receives these rays, he characterised as an electric organ. But heat and electricity are essentially different, and are, in fact, the direct opposites of each other. Electricity is potential energy, heat is kinetic energy : electricity is a power of contraction, heat is a power of expansion. (See Note 21.) The Hertzian waves are undoubtedly a form of heat, but they possess exceptional penetrative power. Hertz proved their refrangibility by passing them through lenses composed of about 14 cwts. of pitch. They appear to be related to ordinary heat waves in the same way as Rontgen rays are related to ordinary rays of light. They also differ from ordinary heat waves by being much longer and less rapid. The waves from a red-hot substance number about 400 million millions per second ; the Hertzian waves are estimated to number about 230 millions. This difference is accounted for by the mode in which they are produced. Every wave consists of an expansion and a contraction, with a consequent interchange of kinetic and potential energy. In ordinary heat the expansions are due to the kinetic energy produced by the collision of the atoms, additional heat being required only to make up for the amount of energy converted into etheric waves. In the case of Hertzian waves the expansions are produced by work done mechanically by means of polarised lines of force. The particles move farther and less frequently than in ordinary heat, but the waves produced are of the same nature, that is, they consist of expansions and contractions of ether. 124 Molecular Forces and Newtonian Laws. A small break in a wire conveying an electric current is called a spark-gap; because, within certain limits, the current passes over the gap and produces a spark at the place. If the gap be made of such a length that the current just does not pass, when Hertzian waves from another discharge pass through the gap a spark is produced. This shows that the Hertzian waves produce polarising effects as if they conveyed electric or magnetic force. But the same effect is produced by ordinary heat waves, only at a much smaller distance. Hertz obtained the same results from solar rays, but only when they were concentrated by means of a lens. Next to the waves from an electric spark, the best results were obtained from the flame of a magnesium wire. The difference, therefore, in this respect, between Hertzian waves and ordinary heat waves is only in degree. Polarising effects can be produced by heat waves from almost any source. (See Note 22.) Marconi's apparatus for wireless telegraphy is constructed on the principle above described. The transmitting instrument produces the waves in a certain pre-arranged order, and the receiving instrument consists of an electric current with a spark-gap of such a length that the current just does not pass. When the waves from the trans- mitting instrument fall upon the gap the current passes, and the message is read the same as by ordinary telegraph. This is merely a particular case of an electric current producing a secondary current in another conductor, as will be explained presently. The great strength of the rays from the transmitting instrument produces the effect at a great distance. The two instruments, however, require to be syntonised, so as to produce an equal number of vibrations in equal time, like two musical instruments tuned to the same pitch. Sharpness is given to the signals Electro- Magnetism and Biamagnetism. 125 by means of a decoherer, which consists of a small hammer worked automatically by the current, and breaks the polarisation within the spark-gap after every passage of the current. 3. Electro-Magnetisation. The action of the Hertzian waves in magnetising an iron or steel bar is very remarkable, as may be observed in the process of making an electro-magnet. When the wire conveying the current is wound round the bar in the direction of a right-hand spiral, the bar is magnetised in the opposite direction to that in which it is magnetised when the spiral is a left-hand one. Or, if a straight wire in a vertical direction be used, the magnetisation is in opposite directions, according as the current passes upwards or downwards in the wire. Heat radiates in all directions, so that the waves from an electric current have the same effect as if they consisted of parallel rings at right angles to the wire. And these waves are the same, both in direction and intensity, in whichever direction the current passes. The mere reversal of the poles, therefore, could have no effect upon the direction of magnetisation unless some lateral effect were produced by the waves. But this implies motion ; for no force can produce any effect without acting through distance. From this it appears that the waves from the electric current are in motion, and that the magnetisation of the metallic bar in different directions is due to the direction in which the heat rays move. The motion of the waves in one or other direction along the wire may also be inferred from the nature of the current. Every electric current consists of a succession of interchanges of potential and kinetic energy, and these 126 Molecular Forces and Newtonian Laws. interchanges necessarily take place along the whole circuit, a heat wave being produced at every interchange. It thus appears that an electric current externally is equivalent to a succession of heat rays in motion. The rate at which the rays move is the velocity of the current, and when an iron bar is placed in its vicinity, these penetrating rays pass through it at the same velocity. Hence the different directions of the magnetisation. It might almost be said that the motion of these Hertzian waves can be rendered visible. When an electric current passes through a long narrow vacuum, a quivering motion is observed, as if waves of some kind were passing along the tube, and that motion is always in the same direction as the current, that is, from the positive towards the negative pole. These facts account for the reversal of the magnetic direction by a reversal of the current. The nature of the action of the waves upon the iron can only be conjectured. That the direct action of heat waves causes a slight separation of the metallic particles we know, and the rapid motion of the waves transversely to their direction obviously produces that polarisation of the particles which is the cause of magnetic force. In the case above supposed, the waves are in motion and the iron bar at rest. The effect would necessarily be the same if the heat waves were at rest and the iron bar in motion. There is thus a very striking similarity between the processes of producing magnetism and electricity. The motion of a magnetic substance through heat waves transversely to their direction generates mag- netism, and the motion of a conductor through magnetic lines of force transversely to their direction generates electricity. The bearing of these simple laws upon the Electro-Magnetism and Biamagnetism. 127 electric and magnetic phenomena of nature is obvious, and this subject will be followed up under the head of Terrestrial Magnetism. The direction of magnetisation, or the direction of a magnetised needle in the vicinity of an electric current, is readily found by Ampere's rule. Let the observer identify himself with a small portion of the current ; if the direction of the current is from his feet towards his head, the needle points to his left ; if the direction is from the observer's head towards ' his feet, the needle points to his right. This rule is applicable in all circumstances. Omitting all reference to an electric current, and assuming the motion of the heat waves to be in the same direction as the current — an assumption which will be verified hereafter by its agreement with natural phenomena — the direction of the needle may be found in all cases by Ampere's rule, whatever the source of the heat waves, by substituting for the direction of the current, the direction in which the waves move, or the opposite direction to that in which the paramagnetic substance moves through the heat waves. When the magnetising heat rays proceed from an electric current, the direction of the needle is always tangential to a circle of which the electric current is the centre. This and some other facts of a similar kind, gave Faraday the impression that magnetic force acts in curves. But the correct interpretation of the fact is, that the position of the needle is always at right angles to the direction of the heat rays. When the heat radiates from a centre, the position of the needle is tangential to a circle, but when the heat rays are parallel, or virtually parallel, like, the solar rays, the direction of the needle is in a straight line. 128 Molecular Forces and Newtonian Laws. The direction of magnetisation is also at right angles to the direction in which the heat rays move, or to the direction in which the magnetic substance moves through the heat waves. Thus the normal position of a bar magnetised by heat is at right angles to the direction of the rays and also to the direction in which the rays move. If by any cause the bar is deflected from that position, the magnetising force always tends to bring it back to the same position again. 4. The Three Magnetic Elements. The small iron bar, or magnetic needle, has hitherto been supposed to be in its normal position, at right angles both to the direction of the current, and to the direction of the heat rays from it. It will be convenient for future reference to consider in this place the effect produced by placing the h&x in different positions with respect to the current and heat waves. Let C C C" be an electric current passing in the direction from C to C". The heat waves are, of course, supposed to move in the same direction. Let NAA'S be a plane normal to the current at C, and coinciding with the rays from the current at that point. Also, let N B B' S be a plane normal to the heat ray at the point P. Electro-Magnetism and Diamagnetism. 129 The line N S, being the intersection of the two planes, is at right angles to the direction of the heat rays, and also to the direction in which the waves move. For convenience of reference that line may be called the viagTietic direction. If a small bar of iron be placed at the point P, the direction of its magnetisation is along the line N S, its north pole being towards N, and its south pole towards S, in accordance with Ampere's rule ; for the current lies behind the plane B B'. If the small bar be turned round in the plane A A', so as to be in the direction PD, it is no longer at right angles to the heat rays, and its magnetisation diminishes accordingly. When it is turned through a right angle its magnetisation vanishes altogether. The angle N P D is called the declination of the magnetised bar, and it is obvious that the magnetising force varies as the cosine of the declination. Again, if the bar be turned round in the plane B B', so that its direction is in the line P I, it is still at right angles to the heat rays, but not to the direction in which they move, and its magnetisation diminishes accordingly. When it is turned through a right angle, so as to be parallel to the direction of the current, its magnetisation vanishes. The angle N P I might be called the inclin- ation of the magnetised bar, but that term is commonly applied to the angle which the bar makes with the direction of the current which is at right angles to the magnetic direction. The angle N P I is, therefore, the complement of the inclination, or the co-inclination of the bar, and the magnetising force varies as the sine of the inclination. Instead of a straight bar, let a small semi-circular bar, N' P S', be brought to the point P, so that the centre of I 130 Molecular Forces and Newtonian Laws. the are may be at that point, and the magnetic direction N S, tangential to it. The bar in this case becomes a horse-shoe magnet, having its poles N', S', in the same direction as the similar poles of the line N S. Since the magnetising force varies as the sine of the inclination, the total strength of the magnet is 2 sin 90° = 2, or the same as that of a straight bar N' S', or a bar of the same length along N S, having its centre at P. The magnet is supposed to be at right angles to the heat waves, but if it be turned round so as to have a declination D, its magnetic intensity will be 2 cos D. Every magnetic force forms a circuit, and in this case the direction of the circuit is from P to N', then through the diamagnetic from N' to S', and again along the bar to P, as indicated by the small arrows. The direction of the force at P is opposite to the direction at N' and S', because they are at opposite sides of the magnetic circuit. If the iron bar were a complete circle, the direction of the force at every point would be tangential to the circle; but, owing to the breai in the magnetic substance, the force acts in straight lines through the diamagnetic between the two poles. This causes a complete change in the magnetic direction between P and N', which we shall now consider. Let S P N be a semi-circular magnet as before, and L any point in it between P and N. It is required to find the direction of the magnetic force at L. Let C be the centre of the circle, and join PC, LC, LS; also draw LA at right angles to P C, and L B tangential to the circle at L. Electro- Magnetism and Biamagnetism. 131 P C L is the inclination of the point L, and L A, A C, the sine and cosine of the inclination. One component of the magnetic force lies along the tangent LB. If the iron circle were complete that would be the direction of the whole force, but owing to the break in the magnetic substance there are lines of force, through the diamagnetic medium, betweeii L and every point of the magnet from P to S. This can be shown by placing a small magnetised needle anywhere within the concavity of the magnet. But all these forces attract the particle L in the same direction, namely, from the line L B towards the line L S, and are therefore equivalent to a single force along that line. The direction of the magnetic force at L is, there- fore, the resultant of two component forces along LB and L S respectively. The former of these is called the horizontal, and the latter the dipping force of the needle. The horizontal force varies from unity at P to zero at N, and the dipping force from zero at P to unity at N. If F be the point where P C and L S intersect, the line L F also varies from zero at P to unity at N. Let that line represent the dipping force at L, and from F draw F R parallel to L B, cutting L C in the point G ; also from L draw L R equal to L C, meeting F R in the point R ; and from R draw R B parallel to F L, and R H parallel to L G. 132 Molecular Forces and Newtonian Laws. Since the total force at L is unity, its magnitude is represented by the line LR, and its direction is the resultant of the two component forces, L F and L B ; therefore B L R is the angle of dip at the point L. The angles L A F and L G F are right angles, and the angles A L F and G L F are equal, each of them being equal to the angle FSC. The two triangles LAF, LGF, are therefore equal in every respect, so that L A = L G. But LG = RH, and by construction LR = LC; and since the triangles LAG and R H L are both right-angled, and have two sides of the one equal to two sides of the other, they are equal in every respect ; therefore the angle H L R is equal to the angle ACL; that is, the angle of dip is equal to the angle of inclination. Also RH and HL are equal respectively to the sine and cosine of the inclination. The line LR is the resultant of the two component forces L F and L B, but it is also the resultant, both in magnitude and direction, of two rectangular forces, LG and LH; and since these are respectively the sine and cosine of the inclination, the dipping and horizontal forces of the needle at any place are as the sine and cosine of the inclination, the direction of the dipping force being along the line L C, or the vertical line as it is called in terrestrial magnetism. When lines of magnetic force pass through magnetic substances, these substances set themselves axially in the direction of the force. This applies also to the particles of a magnetic substance. The direction of magnetic force is the direction of polarisation. This cannot be shown by means of a common magnet, but in terrestrial magnetism, where the atmosphere is the magnet, we get inside of it and can test by means of a magnetised needle the direction Electro- Magnetism and Biaynagnetism. 133 of polarisation. In this way a magnetic needle shows the direction of terrestrial magnetisation, because it necessarily sets itself in the direction of the magnetic circuit. It is necessary to distinguish between magnetising force and magnetic intensity. The magnetising force may be very different at different points of the magnet, but the magnetic intensity is the same throughout the whole circuit. Referring once more to the semi-circular magnet above described (page 130), the magnetising force is at its maximum at P, because at that point the bar is at right angles both to the direction of the heat rays and also to the direction in which they move. At N and S the magnetising force vanishes, because at those points the bar is parallel to the direction of the current. But the magnetic intensity is the same at P as at N and S, because the circuit is of equal intensity throughout its entire length. The dipping and horizontal forces are components of the total intensity, and have no relation to the magnetising force. Their ratio to one another depends solely upon the form of the magnet. The rule above given is applicable to a semi-circular magnet only. Declination, dip, and magnetic intensity are commonly called the three magnetic elements, and any change in these elements in the case of terrestrial magnetism can be shown to be due to the same cause as similar changes in electro-magnetism, the nature of which can be demonstrated at the laboratory table. 5. Magnetisation of Atmospheric Air. Reference has been made hitherto almost exclusively to iron, because that substance is chiefly associated in our minds with magnetism. Other metallic substances possess- ing the magnetic property are either so rare, or possess 134 Molecular Forces and Newtonian Laws. the property in such a low degree, that they attract little notice except in the hands of experts. Atmospheric air, however, is more ubiquitous than iron, -and although its magnetic property is less marked, it performs a most important magnetic function in nature, and accounts for many of those phenomena which, on account of their obscurity, are most perplexing to the observer. The magnetisation of atmospheric air can be most readily shown by means of a solenoid, that is, a helix of, say, copper wire conveying a current of electricity. When a core of soft iron is inserted in the helix, the iron is instantly converted into a magnet. But without any iron core the helix exhibits all the properties of a magnet. It sets itself in the direction of the dipping needle, and attracts magnetic substances the same as an ordinary magnetised steel bar. This effect cannot be due to the copper, because it is one of the most decided non- magnetic substances. The presence of some magnetic substance within the helix is necessary to constitute a magnet, and we seem shut up to the conclusion that the substance is atmospheric air, or some other element contained in it. But oxygen is known to be a magnetic substance, and since the atmosphere is largely composed of free oxygen, there is scarcely room to doubt that the oxygen of the atmosphere is the substance that forms the magnet. Even if the experiment were performed in a vacuum, there would still be magnetic force in and about the helix, because the vacuum is never perfect, and both the Hertzian waves and magnetic force act through the walls of the receiver of the air-pump. In the present state of our knowledge, we may conclude without much doubt, that the magnetic substance is atmospheric air. (See Note 23.) And this conclusion is confirmed by the phenomenon of Electro- Magnetism and Diamagnetism. 135 terrestrial magnetism. The action of a magnetic needle shows that there is present everywhere a magnetic force, not only on the surface of the earth, but at the bottom of the deepest mine, and at the top of the highest mountain. Now, this force cannot be due to two magnetic poles at the extremities of the earth ; for such a force would act according to the law of inverse squares, and the needle would be attracted towards the nearer pole. Neither can the force proceed from the earth ; for it is not a magnetic substance, and cannot form a magnet. All the magnetic matter contained in the earth is so little in comparison with the non-magnetic matter that, even if it were magnetised to its utmost capacity, its effect would be quite inappreciable. Moreover, magnetic matter does not constitute a magnet until it has been magnetised, and no cause is known to exist within the earth sufficient to magnetise any substance contained in it. The magnetisation of the atmosphere solves the problem of terrestrial magnetism. It is a magnetic substance, and a sufficient cause of its magnetisation is known to exist. Heat rays from an electric spark can magnetise it, and so can heat rays from the sun. This is not conjecture — the result was actually obtained by Hertz. He obtained magnetising effects from solar heat, although very feeble compared with those produced by the electric spark. The atmosphere is thus magnetised by the same law as that by which an iron bar is converted into an electro-magnet. Both are due to the motion of a magnetic substance through heat rays transversely to their direction. This magnetisation of the atmosphere accounts for all the facts of terrestrial magnetism. Although there is no source of magnetic force in the earth itself, magnetic force passes through it between the 136 Molecular Forces and Newtonian Laws. poles of the atmospheric magnet, and that force magnetises by induction all magnetic substances contaiaed in the earth's crust. Through any paramagnetic substance contained in the earth's crust the magnetic force is uniform, for it is not distributed over any wider area, but through diamagnetic matter the force is inversely as the square of the distance. 6. Electro-Dynamics. The magnetising effect of an electric current upon atmospheric air gives rise to a number of phenomena which are commonly described under the name of electro- dynamics. A few of these may here be explained. When two parallel conductors conveying electric currents are placed near each other, if the currents are in the same direction the conductors are attracted towards each other ; if the currents are in opposite directions the conductors are " repelled," or attracted in opposite directions. This is accounted for by the magnetisation of the atmosphere by the currents. Let C C be two copper wires conveying currents in the upward direction. By Ampere's rule the magnetic circuits round these currents are in the direction of the arrows A, A'. In the space between the currents the atmosphere is magnetised in opposite direc- tions, and the two circuits tend to neutralise each other. In the space Electro-Magnetism and Diarruignetimn. 137 beyond the currents the magnetic circuits are in the same direction and strengthen each other. Within the field of force formed by the currents, therefore, the position of weakest force is the space between the currents, and the positions of strongest force on the remote sides of the currents. But it is a well known law, the reason of which will be explained hereafter, that diamagnetic substances when placed in a magnetic field move from the position of stronger to the position of weaker force. Hence the two copper conductors move towards each other. If one of the currents be reversed the magnetic circuits are in the same direction and strengthen each other in the space between the currents, which is therefore the position of greatest magnetic force. Hence the copper conductors move away from each other as if repelled. It is obvious that the force acting upon the conductors is not magnetic, but mechanical. The conductors are supposed to be of copper and are not subject to magnetic force, but they lie in a magnetic medium and are displaced by the magnetised air which is attracted from the position of weaker to that of stronger magnetic force. It has been observed that if one of the currents be removed and a magnet substituted in its place, the effect is the same as in the case of two currents. The reason is, that the magnet is itself a magnetic circuit completed through the atmosphere, and acts upon the other circuit the same as if it were produced by an electric current. Two magnets act upon each other in the same way. This is the case previously noted. When a small magnetised needle is placed on a smooth surface near the poles of a strong magnet, there is attraction when the needle foriiis a circuit in the same direction as the magnet, and apparent repulsion when in the opposite direction. 138 Molecular Forces and Newtonian Laws. When two parallel condtictors are placed near each other and a current passes along one of them, a secondary current is induced in the other, in the opposite direction. This secondary current, however, is momentary only ; and when the primary current ceases there is again a momen- tary current in the other conductor, but in the same direction as the primary. Also, when the primary current varies there is a momentary secondary current in the opposite direction when the current increases, and in the same direction when it diminishes. These phenomena are also accounted for by the magnetisation of atmospheric air. Let C C be two parallel conductors placed, say, in the vertical direction, and let a current be supposed to pass along C in the upward direction, it induces a downward current in C. By Ampere's rule, the current pro- duces a magnetic circuit in the direction of the small arrow, A, and that magnetic force passes through the conductor, C, the direction of the lines of force being from the observer's left towards his right. But the direction in which the lines of force move, or in which they are produced when the current begins, is from C towards the observer, and there- fore, by Faraday's law, the current produced in C is in the downward direction. The secondary current is momentary only, because the motion of the lines of force continues only while the process of magnetisation is going on. As soon as the air has been magnetised, the lines are stationary, and no current can be produced. This accounts for the fact that Electro-Magnetism and DiamMgnetism. 139 there is a momentary current as often as there is an increment of the magnetising force, that is, of the strength of the current. The secondary current, which is produced when the primary current begins, is accompanied by heat to a very limited extent only. The reverse momentary current, which is produced when the primary current ceases, is accompanied by a very decided spark, so strong as to be quite formidable in certain circumstances. This shows that the first momentary current consists chiefly in putting the particles of the conductor into the state of potential energy, and therefore requires the expenditure of a certain amount of work. The second momentary current consists chiefly of the running down to heat of the potential energy produced by the first. This point is of considerable interest as showing that the polarisation of the conductor, that is, the putting of its particles into the state of potential energy, proceeds in what is called the positive direction of the current. The reverse motion of the particles, which produces heat, necessarily follows the polarisation. Hence those heat waves from an electric current which produce magnetising effects proceed in that direction also. When an electric current passes through a coil of copper wire, every convolution of the wire produces a secondarj' current in every other convolution. This is called the indijbction of a current on itself.- In such circumstances an appreciable portion of the energy of the current at its commencement is expended in producing that secondarj' current, and when the primary current ceases, a formidable spark is produced, if the current is a powerful one. Hence the dangerous effect of suddenly switching off a strong electric current in such circumstances. 140 Molecular Forces arid Newtonian Laws. This induction of a current on itself has sometimes been called " electrical inertia," because a considerable amount of work is spent in beginning and stopping a current. But inertia is a property of matter, not of force. A more correct analogy may be found in the action of a steam- hammer working in both directions. At the upward stroke part of the energy of the steam is converted into gravitational potential energy, and at the downward stroke that potential energy is again converted into work, and has to be added to the steam-power. In this way also the potential energy produced at the starting of the current is run down to heat when the current ceases. A good illustration of these electro-magnetic forces is afforded by a Ruhmkorff's induction coil, the principle of which must here be assumed to be known to the reader. When an iron core is inserted in the hollow of the coil, the induced current is very powerful, showing that it is due to magnetic lines of force through the coil. When no iron core is inserted, the induced current is feeble, because the only magnetic substance is atmospheric air. The effect is not due to terrestrial magnetic force, for that of itself produces no perceptible current whatever. This shows that the magnetisation of air is intensified by an electric current passing through a coil or helix, as formerly explained. 7. DiAMAGNETISM. Paramagnetic substances set themselves axially between the poles of a magnet, and move towards the nearer pole ; that is, from the position of weaker towards the position of stronger magnetic force. Diamagnetic substances set themselves equatorially, and move away from the nearer Electro-Magnetism and Biamaqnetism. 141 pole ; that is, from the position of stronger towards the position of weaker magnetic force. These facts are well established by observation and experiment. The reason for the position and movement of para- magnetic substances has already been explained ; it remains to account for the position and movement of diamagnetics. These are commonly ascribed to repulsion. It will now be shown that they are due neither to attraction nor repulsion, but to the mechanical action of the magnetised medium in which they are situated. Force and weight are synonymous terms. Iron is said to be heavier than water, because, bulk for bulk, it is attracted towards the earth with greater force. When, therefore, a piece of iron is placed in water, it sinks ; that is, moves from the position of weaker towards the position of stronger force. Timber, on the other hand, is lighter than water, and when placed in that element it rises to the surface ; that is, moves from the position of stronger to the position of weaker force. No one ever dreams of ascribing the motion of the piece of timber to repulsion ; but, being lighter than water, its position is occupied by the heavier element, which, therefore, forces it mechanically to the surface. In these cases we have considered gravitation only, taking no account of magnetic force. Let us now reverse the order, leaving gravitation out of consideration, and taking account of magnetic force only. Iron is magnetically heavier than air, because, bulk for bulk, it is attracted with greater force towards a magnetic pole, and moves from the position of less to that of greater magnetic force when situated in air. Copper is magnetically lighter than air, and moves away from the nearer pole of the magnet; that is, from the position of stronger towards 142 Molecular Forces and Newtonian Laws. Vl A' ^ that of weaker magnetic force. But this is no more due to repulsion than the rising of a piece of timber in water. The position of the copper is replaced by the more strongly magnetic substance, air, and therefore forced mechanically away from the nearer pole of the magnet by the pressure of that element. Let N and S be two magnetic poles, and N S the axial direction between them. Bisect N S in C, and through G draw ECQ at right angles to NS. The line EQ is the equatorial direction; and, being equidis- tant from N and S, is the neutral line between the two poles. If A B be a small bar of copper placed between N and C, it moves towards C, because it is pressed away from N by the magnetically heavier medium air. The copper bar does not, however, move beyond C, because from that point the force again increases towards S. At C the bar coincides with the line E Q ; for if placed obliquely, as A' B', there would be equal and opposite forces at A' and B ', and that couple would turn the bar into the direction E Q. We can now tell the direction and movement of a diamagnetic substance at any point in the magnetic field ; for they are directly opposite to those of a magnetic substance at the same point. At the point C, neither of the substances moves, but the direction of the paramagnetic is axial, and that of the diamagnetic equatorial. At any point along E Q, the paramagnetic moves towards C, and the diamagnetic in the opposite direction along the same Electro- Magnetism and Diamagnetism. 143 line. At any point whatever in the magnetic field the direction of a magnetic substance is tangential to an ellipse of which the magnetic poles are the foci, and therefore the direction of a diamagnetic substance coincides with the bisector of the angle between the focal distances. The motion of a paramagnetic traces a curve towards the nearer pole ; the diamagnetic traces the same curve in the opposite direction. These movements due to magnetic force are, of course, always liable to be modified by gravita- tion, which must be counteracted in some way, in order to show the movement actually due to magnetic force. The mere fact of any substance setting itself in the axial or equatorial direction, and moving to or from the position of stronger force, is no proper test of its being paramagnetic or diamagnetic, but only of its being more or less magnetic than the medium in which it is placed. This rule applies also to gravitational force. Iron sinks in water, but floats in mercury. Liquid air is said to be very strongly magnetic; and if tested in that element it is probable that weak magnetics, such as nickel and cobalt, would set themselves equatorially in the vicinity of a strong magnet, although they set themselves axially when tested in air. (See Note 24.) Diamagnetism affords no evidence of a force of repulsion. All force is inherent in matter, or is by some law essentially connected with it, and by no process short of an act of creation or destruction can that relation be altered. No force, therefore, can exist between any two bodies unless it exists between their respective particles. Upwards of 70 different kinds of substance have been discovered, and among these there is not one whose particles repel each other, or repel the particles of any other substance. No two substances are of such a nature that if the earth were 144( Molecular Forces and Newtonian Laws. composed of the one and the moon of the other, there would be repulsion between these bodies. Between the particles of all substances the force is attraction ; and any combination of these forces must be attraction, on the same principle as any combination of positive quantities, whole or fractional, must be positive. When a piece of copper is brought near a magnet, the fundamental consideration is, whether there is repulsion between the particles of iron and those of copper. Magnetism is only the combined force which resides in the atoms of the iron, and as there is no repulsion between the individual atoms of the two substances, there can be none between them in their combined state. The theory of magnetic repulsion has obviously arisen from a misinterpretation of facts imperfectly understood. There is apparently no such force in nature as repulsion. CHAPTER VI. TERRESTRIAL MAGNETISM. 1. Defective Theories. T?VERY one is familiar, more or less, with the out- -*-^ standing facts of terrestrial magnetism — the direction of the magnetic pole, the variation and dip of the magnetic needle, and the magnetisation of steel bars when placed for a length of time in the direction of the dipping needle. But no scientific account of these facts has ever been given. The various theories propounded on the subject are, for the most part, without any solid foundation in physical law. It has been supposed that the earth may be a great natural magnet. Unfortunately for this theory, there is, properly speaking, no such thing as a natural magnet ; because magnetism is not a property of any known substance. Every magnet is a body which has undergone a process of magnetisation. What are called natural magnets are only substances which have the property of retaining their magnetisation for a great length of time, and have been magnetised by the force known as terrestrial magnetism. Even if it were possible for the earth to form such a magnet, it is manifestly not the case ; because in no sense of the word is the earth a permanent magnet. Its magnetic condition is constantly changing. Within quite recent times its north magnetic pole has 146 Molecular Forces and Newtonian Laws. shifted from north-east to north-west; and that change is obviously due to the same cause as that by which the earth has been magnetised. The process of magnetisation, therefore, whatever its nature, is still in operation. It has been conjectured that the earth may be a great electro-magnet; but we are not told where the electric current, sufficient to magnetise the earth, is generated, or by what power it is maintained. It has also been surmised that the earth may be magnetised hy influence from the sun. Would it be easier to find the origin of magnetism in the sun or moon than on the earth ? Theories of this kind only tell us that their authors are at their wits' end. The most rudimentary knowledge of the subject should be sufficient to satisfy us that the earth proper cannot be a magnet at all. It is not composed of magnetic matter. Neither soil, nor rocks, nor ocean, can be magnetised by means of an electric current or the strongest magnet. Still less can the molten interior of the earth form a magnet, because great heat destroys magnetism. There are, indeed, a few veins of ferruginous rock in the earth's crust, which admit of magnetisation in a limited degree; but even if all these were magnetised to their utmost capacity, they could in no way account for the great magnetic force so equally distributed over the whole earth from pole to pole. To stick a magnetised needle in Ben Lomond would not constitute the mountain a great magnet. The few magnetised substances found in the earth's crust are the effect, not the cause, of terrestrial magnetism. Some misconception on this point seems to have arisen from not distinguishing clearly between a magnet and a magnetic field. Any substance whatever may form a magnetic field, just as any substance may form a field of electric or gravitational force. Two small balls on opposite Terrestrial Magnetism. 147 sides of the earth attract one another, and the whole earth is the field of force between them. In like manner the north and south magnetic poles attract each other through the earth, which is the field of force between them, giving rise to the phenomenon known as the dip of the needle. But there can be no magnetic field without a magnet. A whinstone or a lump of boulder-clay may be a field of force, but cannot- be a magnet. It is impossible, therefore, that the earth as a whole can be a magnet, and the mere fact that it may be a field of magnetic force affords no support to the theory. Another error of universal prevalence is the theory that magnetic force proceeds from two poles, one in the north and the other in the south of the globe. According to this conception, the earth is a great magnet, like a piece of magnetised steel, and the force between its poles acts through the atmosphere, or ether, or some other subtle element, and magnetises all magnetic substances by induction ; for that is the only way in which a substance is magnetised, or attracted, between two magnetic poles. But to this theory there is a fatal objection. Terrestrial magnetism does not conform to the laws of magnetic induction. It has a directive effect upon a magnetised needle, but does not carry it in the direction of either pole. When the needle is suspended by a long silk fibre, it does not deviate in the slightest degree from the perpendicular direction, or when floated on water by means of a small piece of cork, it points to the north but makes no attempt at a northern expedition. Even when carried to the immediate vicinity of either pole, there is no diff'erence in this respect. This is not the law of ordinary magnetic induction. The needle is attracted towards the nearer pole according to the law of inverse squares, and, according 148 Molecular Forces and Newtonian Laws. to that law, the needle at 60° N. Latitude should be attracted in the northern direction with a force about twenty-five times that in the southern. The attempt to explain away this fact by a theory of repulsion is only to call in one error to account for another. The accepted* theory of terrestrial magnetism is essentially at fault, and it is necessary to abandon the cuiTent view on this point, and seek for a correct interpretation of the facts in some other direction. 2. The Atmosphere Magnetised by Solar Heat. A magnetic substance, as we have seen, can be magnetised by the action of heat rays in motion ; or, which amounts to the same thing, by the motion of a magnetic substance through heat rays transversely to their direction. Now, these conditions are fulfilled by the motion of the earth in its orbit. The atmosphere, being largely composed of free oxygen is paramagnetic, and the motion of the earth is at right angles to the solar rays. The velocity in this case — 19 miles per second — though not equal to that of an electric current, is a fair approximation to it, and may be assumed to be sufficient to produce magnetising effects. (See Note 25.) The only point about which there can be any reasonable doubt, is the sufficiency of the solar rays for that purpose. We have seen that the rays from an electric spark cause an electric current to pass through a spark-gap when otherwise it would not pass ; and also that the same effect can be produced by solar rays, but in a much lower degree. The length of gap through which a current passes is in proportion to the strength of the current. It is obvious, therefore, that in these cases the current receives an accession of strength from the action of the heat rays. Terrestrial Magnetism. 149 But this is only a case of the same principle by which the rays from an electric current induce a momentary current in an adjoining conductor. The atmosphere is magnetised by the heat rays, and the motion of the magnetic lines of force transversely to the conductor produce a current, according to Faraday's Law. Marconi's apparatus also takes advantage of this principle by means of wings attached to the receiving instrument, whereby a greater number of heat rays is intercepted. These and other kindred facts show that the difference between Hertzian rays and ordinary heat rays, in respect of magnetising effects, is one of degree only. Solar heat is obviously defective in vibrations of the particular length and frequency necessary to produce the magnetic effect. The atmosphere is magnetised by some natural cause, and we may conclude that the cause is solar heat, although the magnetising force is very small. The feeble magnetising force of solar heat must be taken in connection with the enormous area over which it acts. The strength of a magnetic circuit is the combined strength of all its magnetised particles. When it is considered that the amount of magnetic matter upon which the solar heat acts is equivalent to a layer of iron over the surface of the earth to a depth of 4| feet, it can well be conceived that the total force of the terrestrial magnetic circuit must be far greater than the strength of the magnetising force would lead us to suppose. Assuming, then, the sufficiency of the solar rays to magnetise the atmosphere, let us consider how far the other necessary conditions exist, and how far the results agree with the observed facts of terrestrial magnetism. In conducting these inquiries it will be convenient, for the sake of explicitness, to speak of the magnetic needle in 150 Molecular Forces and Newtonian Laws particular, but it must be understood that what is said of the direction and movement of the magnetic needle is applicable to every particle of the atmosphere, and to every magnetic substance contained in it. The magnetic needle is only one small element of the whole magnetised substance, and follows the same law as all the other magnetised elements. It must be admitted that this introduces a somewhat novel way of thinking about magnetic phenomena. We are accustomed to think of a magnet as a solid body like a bar of steel, and the magnetic field as a rare medium like the atmosphere. In connection with terrestrial magnetism we must accustom ourselves to think of the atmosphere as the magnet, and the solid earth as the diamagnetic between its poles. We do not live in the field, but in the magnet, and the position of a magnetic needle reveals to us the position of all the particles of the magnet. The common theory reverses the necessary order of things. It makes the earth a magnet, which, from its nature, it cannot be, and treats the atmosphere as a diamagnetic, which it can be only for substances more magnetic than itself. The other view which has just been stated puts things in their natural order. The atmosphere is para- magnetic, and forms the magnet ; the earth is diamagnetic, and forms the field of force. This, and other facts to be considered presently, leave no room to doubt that magnetism is an atmospheric, rather than a terrestrial, phenomenon. 3. Direction of Magnetisation. When a needle is magnetised by heat rays from an electric current, the normal position of the needle is at right angles both to the rays and to the direction in which Terrestrial Magnetism. 151 they move. If by any means the needle is deflected from that position it always tends to come back to it again. By this law it is easy to find the direction of terrestrial magnetisation, if it is due to solar heat. The solar rays which fall upon the earth are parallel to the plane of the ecliptic, and since the direction of the needle is at right angles to the rays and also to the direction of the earth's motion through them, the direction of magnetisation must be in a line normal to the plane of the ecliptic, that is, in a line parallel to the axis of the ecliptic. Let the circle N P S be the earth, and K the solar rays, which are virtually parallel, falling upon it. Also, let N S be a line through the centre of the earth at right angles to the solar rays, P P' the terrestrial axis, and NN', SS' the arctic and antarctic circles. If the earth be supposed to move in its orbit either towards the reader or in the opposite direction, the line N S is at right angles both to the direction of the solar rays and also to the direction of the earth's motion through them, and is the direction of terrestrial magnetisation. The line N S is the axis of the ecliptic through the centre of the earth, and its relation to the solar rays and to the earth's motion is the same for all parts of the earth, and for all hours of the day and all seasons of the year. All magnetising force is therefore parallel to that line. 152 Molecular Forces and Newtonian Laws. For this reason magnetic meridians lie north and south, not east and west, along the earth's surface. They do not, however, converge at the terrestrial poles, but at two opposite points in or near the arctic and antarctic circles. Let us now consider which is the positive and which the negative direction of terrestrial magnetisation. Suppose the time to be six o'clock in the morning, the observer's position at that hour is at right angles to the solar rays. Since the earth revolves from west to east, and its orbital motion is the same as that of a chariot of which the earth is one of the wheels. The observer's motion in common with the earth in its orbit is from his feet towards his head, which is the same as if the heat rays moved from his head towards his feet. Turning his face to the west to identify himself with the heat rays, by Ampere's rule, the direction of the needle is to his right, that is to the north. Taking into account the direction of the observer's motion in common with the earth in its orbit, the result is the same for all hours of the day, and for all parts of the earth. Thus, the positive direction of terrestrial magnetisation, if due to solar heat, must be towards the north. If the earth's motion in its orbit were reversed, the needle would point to the south, on the same principle as the magnetis- ation of an iron bar is in the opposite direction when the electric current is reversed. According "to this law the positive direction of magnetisation, at all parts of the earth, is towards the north. If we call the vanishing point in the heavens of all lines parallel to the axis of the ecliptic, the star, that would be the pole-star of terrestrial magnetisation. It might be supposed that the dip of the needle is at variance with the above conclusion ; but it is not so. The distribution of the total intensity of the terrestrial magnetic Terrestrial Magnetism. 153 circuit into a dipping and a horizontal component, depends entirely upon the form of the atmosphere and has no connection whatever with the direction of terrestrial magnetisation. In order to explain this point it is only necessary to repeat the law of electro-magnetisation which has been already stated. Ijet N S be the axis of the ecliptic, E C a section of the plane of the ecliptic,. and the circular portion of the figure a section of the atmosphere, which, being magnetised, forms a semi-circular horse- shoe magnet. At E there is no dip and the needle points to the star, because at that point the surface of the atmosphere is parallel to NS. At N and S the direction of the needle is reversed, because they are on the opposite side from E of the magnetic circuit, the direction of which is from E to N, then through the earth as a diamagnetic to S, and from that point through the magnetic medium again to E. The direction of the needle is necessarily the same throughout the whole circuit, and any magnetic or magnetised substance placed at any point in the circuit sets itself in the same direction. But this change in the direction of the needle, caused by the circular form of the atmosphere, has no connection with the direction of magnetisation, which is always 154 Molecular Forces and Newtonian Laws. parallel to the axis of the ecliptic. The magnetic intensity of the semi-circular magnet is the same as if it formed a straight column of air the length of N S and parallel to that line. At N there is no horizontal force, and the dipping force, or total intensity, is represented by the line N S, or 2 sin 90° = 2, that line being the measure of the semi-circular magnet along the line of magnetisation. If any point L be taken between E and N, and a line drawn from L to C, the dipping and horizontal forces at L are respectively as the sine and cosine of E C L, the sine being measured along the line L 0. This rule gives approximately the direction of the dipping needle at any place, and can be tested by merely suspending a magnetised needle by its centre of gravity. The variations will be noticed hereafter. If the whole figure be supposed to turn round upon its axis NS, it describes a sphere which represents, in a general way, the magnetic condition of the atmosphere. It may be regarded as consisting of a series of semi-circular magnets placed with all their similar poles in contact, so that the total force acts through the earth between the two magnetic poles. No difficulty need be felt about the force acting through the diameter of the earth. Gravita- tional force acts through all substances alike, according to the law of inverse squares, whether the field consists of ether or a granite rock. Magnetic force acts according to the same law, provided there is no polarisation of the magnetic field. This is the general law of force, and it is certain that both electric and magnetic force act according to the same law as gravitation, when there is no polarisation of the intervening medium. In the event of polarisation the whole force is confined to the polarised substance as observed by Hertz. Terrestrial Magnetism. 155 4. Kelation of Needle to Magnetic Poles. In speaking of the relation in which a magnetised needle stands to the magnetic poles of the earth, the mistake is commonly made of reversing the order of cause and effect. The direction of the needle is ascribed to the action of the magnetic poles, whereas the direction of the needle determines the position of the poles. The direction of magnetisation is due to cosmic forces, and the magnetic poles are merely the points where the lines of force pass out of the magnetised substance, the atmosphere, into the diamagnetic medium, the earth. The direction of magnetisation determines the position of the poles, not the position of the poles the direction of magnetisation. The elements of terrestrial magnetic force are' all arranged in the same direction. Every section of the atmosphere, from magnetic pole to magnetic pole, is a semi-circular magnet, and therefore — by the law formerly explained — the direction of the force at any point is the resultant of two component forces which are respectively as the sine and cosine of the inclination. But this is the direction of a magnetised needle ; and since the needle is itself only an element of the magnetised substance on a larger scale than the atoms of oxygen, it necessarily lies in the same direction, for otherwise its poles would be in contact with similar poles of the adjacent particles, and it would be in unstable equilibrium. Hence the magnetic needle shows the direction of terrestrial magnetisation by setting itself in the same direction, not in the opposite direction, as commonly supposed. This proves the point previously stated with regard to the internal condition of a magnetised substance — that 156 Molecular Forces and Newtonian Laws. the positive points of all the atoms lie in one direction and the negative points in the other. The needle shows this to be the condition of magnetised air, and what is true of the atmospheric magnet must be true of all magnets; because the arrangement of its particles is the one characteristic distinction between the magnetised and unmagnetised state of any substance. From the nature of a magnetic circuit it also follows that the north and south poles of a magnetised needle are identical with the north and south magnetic poles of the earth. It is commonly said that the north pole must be a south or negative pole because it attracts the north or positive pole of the needle, and that the pole in the southern hemisphere must be a north pole because it attracts the south pole of the needle. The mistake arises from not observing the nature of a magnetic force, which is always a circuit. The terms north and south, as applied to magnetism, do not denote opposite directions along a straight line, as they do when used geographically, but opposite directions in a circle, like the geographical terms east and west. The magnetic circuit, however, is not round the whole earth, like a geographical circle, but round one hemisphere only, from south to north and then through the earth to the south magnetic pole again. The prevailing mistake on this point has given rise to much confusion in designating the poles of a magnetised needle, and various devices have been adopted to obviate that confusion. French writers reverse the names, calling the north and south poles the austral and boreal poles respectively: some writers in this country call them the north-seeking and south-seeking poles. Faraday adopted the purely conventional terms, marked and unmarked, Terrestrial Magnetism. 157 because the north pole of a magnet has generally some mark placed on it to distinguish it from the south pole. But these devices are unnecessary. The north pole of the needle is a north-seeking pole, because it sets itself in the same direction as all the other magnetised elements of the atmosphere, and that direction is the north. The old popular names, north and south, are still the best, for the north pole of the needle is identical with the north magnetic pole of the earth. The above considerations afford also an explanation of the fact that terrestrial magnetism has a directive effect upon the magnetic needle, but does not transport the whole needle in the direction of either pole. Lying within a magnetised medium, the needle necessarily assumes the same direction as all the other magnetised particles; for if it were turned out of that position, its positive and negative poles would be brought into contact with similar poles of contiguous particles, and would be in unstable equilibrium. Hence the directive force of terrestrial magnetism, which always sets the needle in the same direction as the magnetisation of the atmosphere. But there is no con- vective force, because the forces acting upon the ends of the magnet are equal and opposite. When the needle is placed in the diamagnetic medium between the poles of the magnet, there is a force carrying it towards the nearer pole of the magnet, but when it is placed within the magnet itself, there is no such force. Generally a steel bar will be more strongly magnetised than the atmosphere, and will therefore attract, and be attracted by, the surrounding atmosphere, but theSe forces are always equal and opposite, so that the magnet is not moved out of its place. Hence terrestrial magnetism has no convective effect upon a magnetic needle. This is the explanation 158 Molecular Forces and Newtonian Laws. of a phenomenon which has generally been misunderstood, and which writers on the subject have endeavoured to account for by the theory of magnetic repulsion. 5. Declination and Inclination. When a needle is magnetised by motion through heat rays, the position of the needle is at right angles to the rays and to the direction of its motion through them. Any obliquity to the rays is called the declination of the needle, and the complement of any obliquity to the line of motion, its inclination. The magnetising force varies as the cosine of the declination, and as the sine of the inclination. If the earth moved in its orbit only, or if the terrestrial axis coincided with the axis of the ecliptic, the plane of the ecliptic would be the magnetic equator, and the points where the axis of the ecliptic through the centre of the earth cuts the surface, would be the magnetic poles, that being the only complete diameter of the earth at right angles to the solar rays and to the direction of the earth's motion through them. That diameter corresponds, there- fore, with the line which, in treating of electro-magnetism, we have called the magnetic direction, because it is the normal direction of a needle magnetised by heat rays. The axis of the ecliptic, or line of magnetic direction is, however, a fixed line in space with regard to the earth's motion, and when the earth revolves about the terrestrial axis, the axis of the ecliptic describes a double cone whose apexes are at the centre of the earth, and whose bases are the arctic and antarctic circles. Let the circle of which C is the centre be the earth, PP' the terrestrial axis, N S the axis of the ecliptic, N N' the arctic, and S S' the antarctic circle. Join N' S'. When the earth revolves about PP', the line NS describes the double cone NCN' Terrestrial Magnetism. 159 and S C S'. The basis of these cones N N' and S S' are, properly speaking, the magnetic poles. Every line, such as N' S' from one of these circles, through the centre of the earth, to the opposite side of the other, is a complete diameter which coincides with the axis of the ecliptic once in every 24 hours. This condition is not fulfilled by any diameter termina- ting in a point either north or south of the arctic circle. All such places are, there- fore, of lower magnetic latitude, whether north or south of that line. But magnetisation can take place only along NS, or a line parallel to it, and magnetic force follows the longest axis of a substance, and therefore lies along a complete diameter of the earth. For this reason the magnetic pole is situated in, or near, the arctic circle, but may occupy any position in that circle. As a matter of fact, it moves round the arctic circle, and the cause of that motion we shall see presently. Every terrestrial meridian is subtended by a diameter which coincides with the axis of the ecliptic once in every 24 hours, and that diameter is the magnetic direction for all places situated on that meridian. The diameter N' S', for instance, subtends the meridian P S P', and since it coincides with N S once in 24 hours, it is the direction of 160 Molecular Forces and Newtonian Laws. magnetisation for all places, such as L, situated on that meridian. For this reason the inclination of any place must be measured along the terrestrial meridian of the place, and is the distance of the place from the magnetic equator, that is, the latitude of the place plus 23° 30' when the plane of the ecliptic is the magnetic equator, but the position of the magnetic equator is constantly changing. The declination of the needle is measured on a great circle through the terrestrial pole at right angles to the meridian of the place ; or, as it may be called, the transverse meridian of the place. When the direction of the needle is east or west of the meridian it is no longer at right angles to the solar rays, and the magnetic intensity diminishes accordingly. When the magnetic pole is in the meridian of any place, the declination vanishes, and is at its maximum when the magnetic pole is in the transverse meridian. At the ecliptic the maximum declination is 23° 30', or the radius of the arctic circle, and increases to 90° at the arctic circle. Beyond the arctic circle declination has no effect upon the magnetisation of the needle. Inclination and declination affect the magnetising force only ; the dipping and horizontal forces are regulated by the form of the magnet. The former relate to the process of making the atmospheric magnet, the latter to the nature of the magnet after it has been made. The space within the arctic circle adds nothing to terrestrial magnetisation, because every diameter of that circle is reversed every 24 hours, so that whatever magneti- sation takes place in one direction is neutralised by opposite magnetisation in the other. The magnetic intensity within the arctic circle is, however, the same as that of the adjoining atmosphere, because it possesses the magnetic Terrestrial Magnetism. 161 property and is magnetised by induction. The effect is the same as when a piece of iron is laid upon one of the poles of a magnet. The iron adds nothing to the strength of the magnet, but forms part of the circuit and affects the dipping and horizontal components of the magnetic force the same as if it were a part of the magnet. 6. Movement of Magnetic Pole. If the atmosphere received and parted with magnetisa- tion very rapidly, like soft iron, the magnetic pole would always remain at the point where the axis of the ecliptic cuts the earth's surface, and would make a complete revolution of the arctic circle once in twenty-four hours, from east to west, or in the opposite direction to that of the earth's motion. If the atmosphere did not receive and part with magnetisation at all, the magnetic pole would occupy a fixed position in the arctic circle, and would revolve along with the earth without any change of position whatever. The actual state of the case lies between these two extremes. The magnetic pole moves, but very slowlj', making only one revolution in the course of several centuries. It thus appears that the magnetic property of the atmosphere is more akin to that of hard steel than of soft iron. From this property of atmospheric air it is obvious that, if once magnetised, the atmosphere must retain its magnetised state for a considerable length of time. By the direction of terrestrial magnetisation at any given time, therefore, must be understood the direction in which the magnetic needle would continue to point if the action of the magnetising force were to cease. And this is all that is meant by the magnetic pole. It is the direction L 162 Molecular Forces and Newtonian Laws. of terrestrial magnetisation for the time being. But that direction is constantly undergoing change by the action of magnetising force in a different direction. To this cause is due the recession of the magnetic pole, or its motion in the opposite direction to that of the earth's revolution. The normal direction of the needle is at right angles to the solar rays, so that there is always a force tending to set the needle in the direction of the axis of the ecliptic ; that is, along the meridian of any place, which is subtended by the axis of the ecliptic once in every twenty-four hours. But by the revolution of the earth, every element of the atmosphere is carried round the terrestrial axis with its magnetisation as it is for the time being. The magnetic pole thus revolves with the earth, but is gradually changing its position according to the strength of the magnetising force, that is, according to the strength of the solar rays. When a magnetised needle is suspended in the vicinity of an electric current, it assumes a position tangential to a circle of which the current is the centre, and when the needle is turned out of that position it always returns to it again. It is the same force — namely, the tendency of the needle to set itself at right angles to the magnetising rays — that causes the motion of the magnetic pole. Let the figure represent the earth as before, the letters also having the same signification. If the magnetic pole be at N', and L any place on the meridian PLP', the small arrow shows the direction of the needle at L. But the meridian PLP' is transverse to the solar rays, and the needle tends to take up a position parallel to that line, or rather to the diameter through the earth's centre from the arctic to the antarctic circle, by which Terrestrial Magnetism. 163 the meridian is subtended. Owing t6 the nature of the atmosphere the change of direction takes place very slowly, but it is accomplished at last. The needle, and the magnetic meridian of which it shows the direction, coincide with the terrestrial meri- dian PLF; that is, the magnetic pole has moved from N' to the point where the meridian P L P' cuts the arctic circle. But the same action takes place at every meridian, so that the tendency of the needle to set itself at right angles to the solar rays causes in the course of time a complete change in the direction of terrestrial magnetisation. Any increase in the intensity of solar heat tends to accelerate the movement of the magnetic pole, and to this cause may be traced certain variations of the magnetic needle. These variations are only temporary, but if the sun's heat were permanently increased, the result would be a constant acceleration of the movement of the magnetic pole. If very accurate observations could be taken, a record of the total solar heat for the year might be found in the recession of the magnetic pole ; for the greater the volume of heat the greater must be the movement of the pole throughout th« year. It is probable, however, that 164 Molecular Forces and Newtonian Laws. in certain conditions of the sun's surface the solar heat contains a greater proportion than in others, of those rays upon which magnetisation depends. From the nature of the causes, it should be possible to form a fairly accurate estimate of the movement of. the magnetic pole, and of its position at any given time. In the year 1657, the needle pointed due north at London, so that the magnetic pole must at that time have been in the meridian of that place, or very near it. In the year 1831, Captain Ross located the magnetic pole in 96° 45' W. longitude. Since the magnetic pole took 174 years to pass through that angle, a complete circuit should occupy about 647 years. This is probably a fairly close approxi- mation to the period of revolution, and it is confirmed, as we shall see hereafter, by the variation of magnetic dip. According to this calculation, the position of the magnetic pole at the present time (1905) should be about 136° W. longitude, and the direction of the needle should again be due north at London sometime before the end of the present century, probably about the year 1980, the magnetic pole being then on the opposite side of the arctic circle. Change in the direction of atmospheric magnetisation is due to causes which are constant in their operation. The earth's motion in its orbit is perfectly steady, and the magnetic property of the atmosphere is not subject to change. Although the intensity of solar heat varies from hour to hour, and from season to season, the total volume of heat from year to year is virtually a constant quantity. If the diamagnetism of the earth were uniform, the move- ment of the magnetic pole from year to year would be constant. This, apparently, is not the case; and since force always follows the shortest course, the magnetic pole Terrestrial Magnetism. 165 lingers over those parts of the earth's surface where there is the greatest degree of polarisation, and passes more rapidly over those parts where the diamagnetic property is more nearly perfect. 7. Variation of Declination. The great secular changes of declination are due to the motion of the magnetic pole round the arctic circle. From this cause the needle has alternately an eastern and a western declination, each of about 324 years' duration. The declination due to this cause should vary as the sine of the angle through which the magnetic pole moves, but irregularities are caused b}' changes of the magnetic meridians. The magnetic needle does not generally point directly to the magnetic pole. The needle has also small annual and diurnal variations, from two or three to as much as twenty or twenty-five minutes in length. In this country, at the present time, these variations are always towards the west. They diminish in length towards the south, and disappear altogether in equatorial regions. Their origin may probably be traced to refraction. If the solar rays passed in straight lines through the atmosphere, they would always be normal to the axis of the ecliptic, and the magnetic direction would be parallel to that line. But, owing to the convexity of the atmosphere, the solar rays are bent towards the earth, and the needle is deflected towards the terrestrial axis. Let the semi- circle in the figure be the northern hemisphere, E E' the ecliptic, C P the terrestrial axis, C N the axis of the ecliptic, and E. the solar rays refracted by the atmosphere. If the rays passed in straight lines through the 166 Molecular Forces and Newtonian Laws. atmosphere, they would be normal to CN, and the direction of magnetisation would be parallel to that hne. But the rays are deflected in an increasing ratio from E c e E to N, and are normal to the curved line C N', which is therefore the direction of magnetisation. Thus, by refraction, the needle is deflected towards the terrestrial pole. This is probably the reason why the north magnetic pole is not situated in the arctic circle, but about 3° 35' north of it, as observed by Ross in 1831. Owing to its revolution the arctic circle is not permanently magnetised by the solar rays ; but if the position of the magnetic pole is due to refraction, the space within that circle must be permanently magnetised so far ; because the efiiect is the same as if the arctic circle were situated so much farther north. Refraction depends upon the density of the atmosphere as well as its obliquity to the solar rays ; and since the atmosphere is slightly rarefied by the heat of summer and by the direct rays of the sun during the day-time, its refractive power is thereby diminished. To this cause may be traced the small annual and diurnal variations of the needle. From the nature of the case, these variations are Terrestrial Magnetism. 167 to a certain extent a reversal of the effect of refraction, and the direction of the needle is therefore away from the terrestrial axis. At all places having a westerly declination these variations are, therefore, to the west, and to the east at all places having an easterly declination. And since refraction increases according to latitude, these variations diminish and practically disappear in equatorial regiors. This agrees with observed facts. (See Note, 26). Variations of the magnetic needle are also caused by suddei: changes in the intensity of the solar rays. The actual direction of the needle is at all times a state of equilibrium between two forces, the direction of terrestrial magnetism for the time being, and the magnetising force of solar heat. Any change in the ratio of these two forces must caase a corresponding change in the direction of the needle. Sudden changes in the intensity of solar heat appear to be caused, either by the falling of great masses of meteoric matter into the body of the sun, or by an eruption of condensing solar matter. To one or other, or both, of these causes appears to be due the phenomenon of sun-s2>ots, and at such times variations of the magnetic needle are specially observable. But whether there are sun-spots or not, any sudden increase in the intensity of the solar rays must have the same effect upon the magnetic needle. From -jhe nature of the case, these variations are in the direction of the star ; that is to say, the needle tends to set itself parallel to the axis of the ecliptic, wherever it may be at the time. The axis of the ecliptic passes through every point in the arctic circle at noon, so that the direction of the variation depends upon the hour of the day and the position of the magnetic pole. If a line be drawn from any place to the point where the axis of 168 Molecular Forces and Newtonian Laws. the ecliptic cuts the arctic circle at the time of the sudden increase of solar heat, the variation is to the east or ^yest according as that line is to the east or west of the magnetic meridian of the place. / In all these cases of variation caused by increased intensity of the solar rays, account has to be taktn of refraction ; because the direction of magnetisation lis at right angles to the rays, however much they may be deflected. At the arctic circle the solar rays are visually horizontal, and the deflection is very great, accord/ng to the law of earth refraction. The same effect is olJserved in the case of Hertzian waves when used in yireless telegraphy. These waves are transmitted hori4)ntally, and but for refraction they would pass out of the atmosphere without touching the receiving instrument, if the (listance were very great. In order to convey a message to i station on the opposite side of the Atlantic, the rays ffom the transmitting instrument must be deflected 3s or 40 degrees by refraction. In arctic regions the solar rs similarly deflected by the same law, and a line angles to these rays is in a very different direct ( the axis of the ecliptic. For this reason the dii action of the variation in these far northern regions may )e in the opposite direction to what would be expected by the rule above given. Dr. Nansen, in " Farthest North," mentions thai on 24th November, 1894, about 6 o'clock in the evening, t'le officer in charge of the magnetic observations was startled by a remarkable variation of the needle, amounting to S^° to the east. The Fram was then about 82° N. latitude and 114° E. longitude. Nansen does not mention the declination of the needle, but, from the position of the niagnetic pole, it was in all probability to the east. I^ these ays are at right on from Terrestrial Magnetism. 169 circumstances a variation to the west was to be expected, but the variation to the east can be readily accounted for by refraction of the solar rays. For the same reason, if the variation had occurred at 6 o'clock in the morning, it would have been to the west, when an easterly variation was to be expected. This magnetic peculiarity of arctic regions can be expressed very simply by mathematical symbols. We have seen that the magnetising force of the solar rays varies as the sine of the inclination. At 90° the force is at its maximum, and at 180°, that is, when the heat rays are parallel to the magnetic substance, the force vanishes. At 180° the sine passes through zero, and beyond that point the sine is negative, that is, the needle is turned in the opposite direction. When the heat rays are straight lines, the zero point is at the arctic circle, because the rays are there parallel to the surface of the atmosphere. When the rays are bent by refraction, the zero point is somewhere north of the arctic circle, where the rays are parallel to the surface of the atmosphere. This latter point marks the true arctic circle for magnetic calculations. The great length of these variations in arctic regions is due to the magnetic direction, which is nearly vertical. The magnetising force is horizontal, and when the needle is in the vertical direction it offers the minimum of resistance to the horizontal force, which is directive but not convective within a magnetic substance. This may be illustrated by placing a beam of timber in water. The force which is sufficient to turn the beam round horizontally when held in the vertical direction would scarcely move it when placed horizontally on the water. The horizontal component of magnetic power is a retaining force in so far as the gyration of the needle is concerned ; and since that 170 Molecular Forces and Newtonian Laws. component varies from zero at the magnetic pole to unity at the magnetic equator, the variation produced by any change of the magnetising force must be inversely as the horizontal component of magnetisation for the time being; that is, the variation diminishes from the magnetic pole to the magnetic equator. All these variations of declination, to whatever cause due, are temporary only. They do not produce any permanent change in the direction of terrestrial magnet- isation. As soon as the disturbing cause ceases to act, the atmosphere returns to its former condition ; just as a magnetised needle, when affected by the proximity of a magnet, returns to the polar direction as soon as the disturbing cause is removed. 8. Variation of Dip. The term, dipping force, is used in terrestrial magnetism to denote the force of attraction, through the earth, between the magnetic poles. Between every particle of the atmosphere in the north, or positive, arm of the magnet, and every particle in the south, or negative, arm, there are lines of force varying in intensity from zero at the magnetic equator to a maximum at the poles. The resultant of all these forces is the direction in which the atmosphere is magnetised, and is indicated by the dipping needle. Every atmospheric magnet is a semi-circle, and, if the magnetic equator were always at the centre of the semi- circle, the dip would vary regularly as the angle of inclination. This condition, however, is very rarely fulfilled. From the plane of the ecliptic the magnetic equator moves northward as far as 9° 9', returning to the ecliptic after a period of 324 years. It then moves Terrestrial Magnetism. 171 southward to the same distance, and returns once more to the ecliptic after a similar period, thus making a complete cycle of movements in the same period as one revolution of the magnetic pole. The cause of these movements, and the accompanying variations of magnetic dip, will now be explained. In the accompanying figure let the circle represent the earth, PP' the terrestrial axis, and NS, N'S' two diameters at opposite sides of the arctic and antarctic circles ; also, let E E' be the plane of the ecliptic, Q Q' the equator, and M M' a circle between the ecliptic and equator, 9° 9' from the former, and 14° 21' from the latter. Join N S', and draw S' A at right angles to N S, also small tangents to the circle at N and S'. If we suppose the magnetic poles to be at N and S, the whole magnetising force consists of the solar rays falling upon the arc N S', because the circle S' S revolves once in every twenty-four hours, and adds nothing to the 172 Molecular Forces and Newtonian Laws. magnetising force. The total magnetic force, therefore, is represented by the line N A, that is, sin 90° + sin 43° = 1-68. But in every magnet the positive and negative elements are equal, which gives for each hemisphere a force of "84, or 'ISQ less than unity; and since '159 = sin 9° 9', the magnetic equator is situated 9° 9' north of the ecliptic, and 14° 21' south of the equator. Its position, therefore, is represented by the line M M' in the figure. The magnet NMS' is not uniformly magnetised, the southern arm being of greater magnetic intensity than the northern, so that the equator M C is not at its centre. This, however, does not affect the dip, or angle at its extremities, which is 66° 30', as shown by the small tangential lines at N and S'. Thus the dip at each pole is just half the length of the whole magnet. The atmosphere from S' to S forms no part of the magnet, but serves to equalise the length of the two arms and raise the dip to 90°. The effect is the same as when a steel magnet is made with arms of unequal length, and a piece of soft iron is placed on the shorter arm to make it of the same length as the other, so that the lines of force between them are at right angles to the horizontal at both poles. Since the angle of dip is just half the entire length of the magnet, it is obvious that when a bar of magnetic substance is placed upon one of the poles of the magnet, the alteration of dip is half the length of the bar. Thus, in the figure, the distance from S' to S is 47°, but the difference of dip due to the circle is only 23° 30', as shown by the angle S' N S, which is only half the angle S' C S, the one being at the circumference and the other at the centre of the circle. This law is purely geometrical and applies to all semi-circular magnets. If L be any place situated on the meridian P Q P', the Terrestrial Magnetism. 173 left-hand side of the figure represents the magnetic condition at L, and all other places on the same meridian, when the magnetic pole is in that meridian. The right- hand side of the figure represents the magnetic condition at L, and all other places on the same meridian, when the magnetic pole is on the opposite side of the arctic circle. The figure thus shows that when the magnetic pole is in the meridian of any place, the magnetic equator is 14° 21' south of the .equator on that meridian, and when the magnetic pole is on the opposite side of the arctic circle, the magnetic equator is 14° 21' north of the equator. The magnetic equator, therefore, makes a total variation from south to north, and from north to south, of 28° 42'. But this represents a variation of dip to the extent of 14° 21' ; for the variation of dip is only half the length of the arc. When the magnetic pole moves round the opposite side of the arctic circle towards N', the magnetic equator begins to move southward, and when the magnetic pole reaches N' the magnetic equator again moves northward. The difference between maximum and minimum dip at the arctic circle is therefore 14° 21'. But the variation of dip is the same at all places along the same meridian, because the variation of distance from the magnetic equator is the same for every place. The only difference,^ therefore, between the magnetic dip at any point in the arctic circle and any place on the same meridian is the difference of latitude between them. At the arctic circle the maximum dip is 90°, or the latitude of the circle plus 23° 30'. Hence the rule for all places : the maximum dip is the latitude of the place plus 23° 30', and the minimum dip is the latitude of the place plus 9° 9'. This rule is subject to correction for the distance of the magnetic pole north of the arctic circle. The locus of the 174 Molecular Forces and Newtonian Laws. magnetic pole is a circle in which any diameter of the earth at right angles to the solar rays cuts the surface. Theoretically that locus is the arctic circle ; but owing to the deflection of the solar rays by refraction it lies about 3° 35' nearer the terrestrial pole. At the magnetic pole the dip is 90°, and therefore at all places south of the magnetic pole, as far as the solar rays are perceptibly affected by refraction, the dip is somewhat less than it would be if the magnetic pole were situated in the arctic circle. There are also local causes which may increase or diminish the dip of the needle at any given place, but at London the combined effect of all these causes does not appear to be more than about 18', by which amount the dip is less than normal. The latitude of London is 51° 30' very nearly, and the maximum dip, according to the rule, should be 51° 30' + 23° 30' = 75°. About the year 1723 the observed dip was 74° 42', which is a very close approximation to the theoretical maximum, the difference of 18' being probably due to the position of the magnetic pole. The minimum dip at London should be 51° 30'+9° 9' = 60° 39', or after a correction of 18', 60° 21'. No observation of the minimum dip at London has ever been taken, but the rule can be tested by the variation from time to time. The total variation is 14° 21', and that takes place in about 324 years, giving an average annual variation of 2-6574'. Although the variation of dip seems to proceed by fits and starts, when a great number of years are taken together the product by the average annual variation gives a very close approximation to the results of observation. The maximum dip at any place is not synchronous with the passage of the magnetic pole through the meridian of Terrestrial Magnetism. 175 the place, but follows it in much the same way as the spring and neap tides follow the course of the moon, only at a much greater interval. The magnetic pole passed through the meridian of London in 1657, but the magnetic dip did not reach its maximum till the year 1723, an interval of 66 years. The cause of' this slow progress of magnetic dip is quite intelligible. The direction of magnetisation is due to the force of attraction between the north and south arms of the atmospheric magnet, and as the air undergoes change of magnetisation very slowly, a great length of time elapses before it assumes the new direction. In taking observations of magnetic dip it has to be kept in mind that the observed dip does not correspond with the position of the magnetic pole at the time of observation, but with its position about 66 years before. Beckoning the variation of dip from 1723, let us compare with observation the result in 1885, that is, 162 years after the maximum, and when half the fall should have taken place. Multiplying the average annual fall by the number of years, we get 2-6574' x 162 = 7° 10-5', or half the total variation. Deducting this from the maximum, we get 74° 42' -7° 10-5' = 67° 31-5'. The actual reading at London for that year was 67° 38'. Taking other dates, the agreement is sometimes closer, sometimes wider of the mark, but the results, as a whole, afford a strong pre- sumption in favour of the rule. By calculating on the same principle it appears probable that the magnetic dip will reach its minimum at London about the year 2047, and that it will then be about 60° 21', or 18' less than the theoretical minimum, making that allowance for the effect due to the position of the magnetic pole, combined, perhaps, with that of the magnetic constant of the place. 176 Molecular Forces and Newtonian Laws. 9. Magnetic Intensity. The difference of magDetic intensity at different parts of the earth's surface is caused by unequal magnetisation. If the terrestrial axis coincided with the axis of the ecliptic there would be practically the same intensity at all parts of the earth, but, owing to the different positions of the magnetic pole with respect to the direction of magnetisation, the atmosphere is magnetised more intensely at some places than at others. We have seen that magnetic intensity varies as the cosine of declination. The reason of this is obvious. When there is no declination all the heat rays pass through the magnetic substance, but when the rays fall obliquely upon the substance the number of rays passing through it is as the cosine of obliquity. The dii-ection of magnetisation at any place is along the meridian of the place, because the diameter subtending the meridian coincides once in 24 hours with the axis of the ecliptic. When, therefore, there is declination to the east or west of the meridian, the magnetising force is as the cosine of the declination. Magnetic intensity is thus greatest along the meridian of no declination, and least along the meridian of greatest declination ; and these meridians are at right angles to each other. In other words, magnetic intensity is greatest at any place when the magnetic pole is in the meridian of the place, and least when the magnetic pole is in the transverse meridian. But there is a counter influence to this effect of declination. The total magnetising force of the solar rays is greater at any place when the magnetic pole is in the transverse meridian than when it is in the meridian of the place. This will be readily understood from Terrestrial Magnetism,. 177 the accompanying figure, which is the same as before, only instead of supposing the magnetic pole to be at N, in the meridian P N P', it is now supposed to be at N", in the meridian PN"F. These meridians are at right angles to each other, and at any place, L, on the meridian PNP', the declin- ation is at its maximum, but the magnetising force is also at its greatest, and counteracts to some extent the efifect of declination. When the magnetic pole is at N, the magnetising force consists of the solar rays falling upon the arc N S', and, since there is no declination, the total magnetic intensity along the meridian is sin 90° + sin 43 = 1 'GS. When the magnetic pole is at N", the magnetising force consists of the rays falling upon the arc N" S", and the total magnetising force is 2 sin 66° 30'= 1'834. But since there is a declination, say D, the actual magnetising force is 2 sin 66° 30' x cos D. At the ecliptic, which is then the magnetic equator, D = 23° 30', and therefore at the point where the meridian P L P' cuts the ecliptic, the mag- netising force is the same whether the magnetic pole is at N or N",because sin 90° -|- sin 43° = 2 sin 66" 30 x cos 23° 30'. But the declination increases fi:om 23° 30' at the ecliptic to 90° at the arctic circle, so that the total magnetisation M 178 Molecular Forces and Newtonian Laws. along the meridian PLP' is much greater when the magnetic pole is at N than when it is at X" Hence the magnetic intensity is at its maximum along any meridian when the magnetic pole is in the meridian, and at its minimum when the magnetic pole is in the transverse meridian. It has also been ascertained by observation that magnetic intensity increases from the magnetic equator towards the poles. In arctic regions the force is fully twice as great as it is in equatorial regions. This effect, however, is not due to any inequality of magnetisation, but to the form of the atmosphere, which is a hollow sphere. Every magnetic force is equal throughout the whole circuit, and since that force is distributed over a much greater area at the equator than at the arctic circle, the intensity must be proportionately greater in the northern region. The circumference of the earth at the equator is to the circumference of the arctic circle as five to two, and the magnetic intensity at any point must be inversely as the area over which the total force is distributed. This makes the intensity in arctic regions about two and a half times what it is at the equator, and the theory in this respect agrees very closely with the results of observation. It is necessary to distinguish between magnetic intensity and the intensity of magnetising force. There is no magnetising force within the arctic circle, but the total force is the same as at any other part of the circuit. The atmosphere within the arctic circle is magnetised by induction between the two poles, in the same way as a piece of soft iron is magnetised between the poles of an ordinary magnet. The total force being the same, the intensity is also inversely as the area over which the Terrestrial Magnetism. 179 force is distributed. In this way there is great magnetic intensity in arctic regions although there is no magnetising force. All the outstanding facts of magnetic intensity are thus fully accounted for. It is commonly said that there are two centres of greatest intensity in the northern hemi- sphere — one in the north of America and the other in the north of Siberia. These are manifestly the two regions of no declination ; for during the last century, in the course of which such observations have chiefly been taken, the magnetic pole has been in the north of America, and therefore the meridians of no declination have been in the regions described as the centres of greatest intensity. They are not, however, fixed localities, but move westward in common with the magnetic pole. It is probable that they follow the course of the magnetic pole at an interval similar to that of maximum magnetic dip, for a substance which changes its magnetisation slowly is also slowly magnetised. It is also observed that the intensity of the American centre is greater than that of the Siberian. This is necessarily so, because the American centre is in the vicinity of the magnetic pole, where the total force is focussed within the narrowest compass, whereas the whole arctic circle lies between the pole and the Siberian centre, so that the force is there distributed over a much wider area. 10. Magnetic Irregularities. What has been stated above is the mathematical theory of terrestrial magnetism ; but observed facts present only a rough approximation to it. If the atmosphere were a perfectly homogeneous magnetic substance, and the earth 180 Molecular Forces and Newtonian Laws. perfectly diamagnetic, the declination and dip of the needle would correspond very closely with the mathematical rule ; but these conditions are not fulfilled, and hence the apparent irregularities. With regard to declination, many of the irregularities are apparent rather than real, because they proceed from the operation of constant laws. The direction of the needle, and therefore of the magnetic meridian, at any place, is the resultant of two forces. One of these is the force of terrestrial magnetism as it is for the time being, and is in the direction of the magnetic pole. But for the spherical form of the atmosphere that force would be uniform, but owing to the contraction of the area over which the force is distributed, it is about two and a half times greater at the pole than at the equator. The other force is the action of the solar rays, and is always normal to the arctic circle. It is at its maximum at the ecliptic and vanishes at the arctic circle, where the atmosphere has no inclination. From the action of these two forces it is obvious that magnetic meridians cannot be straight lines. At the ecliptic they are subjected to a strong force parallel to the terrestrial meridians, and while that force diminishes in the northern direction, there is an increasingly strong force in the direction of the magnetic pole. All magnetic meridians are therefore curved lines, and give very little idea of the position of the magnetic pole, unless the curva- ture of the meridian is known. Seeming irregularities of declination are thus produced by the regular operation of magnetic laws. The effect of magnetisation on the declination of the needle is specially marked on that side of the earth where all the magnetic meridians pass through the arctic circle. Terrestrial Magnetism. 181 The magnetising force on that side is very strong, because the magnetic equator is 9° 9' south of the ecliptic, and the whole magnetisation takes place within 52° 9'. The mag- netic meridians are consequently very nearly parallel to the terrestrial meridians, or normal to the arctic circle. Within that circle there is no permanent magnetisation, and the magnetic meridians pass through it in straight lines, very nearly. The tendency of magnetic meridians in that part of the earth is, therefore, to assume the form of straight lines, with a sharp bend at the arctic circle. The effect of this peculiarity is to greatly modify the ■ declination of the needle, sometimes even to make it easterly when it should be westerly, and vice versa. Let N A A' be the arctic circle, N the magnetic pole, P the terrestrial pole, and NPB the meridian of no declination. Also, let NAL and NA'L' y- X. l be two magnetic meridians with a sudden bend at A and A', and draw LN' tangential to the meridian NAL at the point L. The side of NB towards L is the h,emisphere of eastern declination, because in looking towards P from any point on that side of N P, the point N is to the right or east. But the needle at L points to N', and has a small western declination. Thus, at places on the meridian NAL south of A, the needle has a small western declination, but within the arctic circle the declination is to the east. Along the meridian N A' L' the effect is reversed. Towards L' the needle has 182 Molecular Forces and Newtonian Laws. a small easterly declination, but within the arctic circle the declination is to the west. This is the explanation of the fact that a great part of eastern Asia has a small western declination, although situated in the hemisphere of eastern declination. The magnetic pole should be in the meridian of London, but on the opposite side of the arctic circle, sometime before the end of the present century. When the magnetic pole is in that position the magnetic meridian of London will pass through the whole breadth of the arctic circle in which there is no magnetisation, but south of that circle it will be subjected tp a strong magnetising force in the direction of the terrestrial meridian. The apparent motion of the magnetic pole may, therefore, be very irregular. The needle may even vary between an eastern and a western declination. These seeming irregularities are not due to the actual movement of the magnetic pole, but to variations of the magnetic meridian caused by a change in the ratio of magnetic forces. Irregularities of dip are accounted for by irregularities of the earth's diamagnetism. If the substance of the earth were perfectly homogeneous the lines of force would every- where pass through it in straight lines. This, however, is not the case. Scarcely any two substances are exactly alike in their diamagnetic property ; and since magnetic force follows the shortest course, the action of that force through the earth varies in direction and intensity according to the nature of the substance through which the lines of force lie. There are a few veins of magnetic matter in the earth's crust, and other rocks on a much larger scale which, though not generally reckoned paramagnetic, are better conductors than others of magnetic force. Wherever such substances Terrestrial Magnetism. 183 exist near the earth's surface, they necessarily affect not the dipping force only, but also the horizontal force, for some distance around them. Hence nearly every place has its own magnetic constant; that is, it gives a certain bias of its own to the direction of the magnetic needle, in addition to that which is due to general cosmic forces. There is a difference between land and water in this respect. Water is almost a perfect diamagnetic; earth and rocks, for the most part, form a stronger field of force. A different magnetic reading is often obtained according as the observation is made on shore or on board ship at a little distance from land. Any great difference in the earth's diamagnetism at different parts would materially affect terrestrial magnetic force, just as the force of a horse-shoe magnet is materially affected by placing an iron bar in different positions between the two arms. It is probable, however, that these irregularities are limited to a short distance from the earth's surface. Throughout the greater part of the interior it is probable that there is little or no difference in the di9.magnetic property. Some facts would incline us to think that the earth is more magnetic towards the centre than towards the surface. It is probable that to these causes may be traced the relative position of the magnetic poles to each other, and to the arctic and antarctic circles. The atmosphere being a spherical body of homogeneous magnetic matter, can have only two magnetic poles, or points, at its surface ; and these must lie beyond the arctic and antarctic circles respec- tively ; meaning by these terms the lines up to which the atmosphere is permanently magnetised by the solar rays, whether in straight lines, or as deflected by refraction. Now, if the earth were a perfectly uniform diamagnetic 184 Molecular Forces and Newtonian Laws. substance, the magnetic poles would be at these circles, because the distance between them is the least possible, and that is always the line of diamagnetic force. If, how- ever, the diamagnetism of the earth is unequal, the force may find a shorter course by partial polarisation in some other direction. Land forms a stronger field of force than water, and as the arctic circle lies almost entirely over land, the north magnetic pole appears never to move very far from that circle as above defined, but moves round it with comparative regularity. The antarctic circle lies almost entirely over water, and the force seems to find a line of greater intensity through the great table-land which lies towards the terrestrial poles, far south of the antarctic circle. The magnetic poles do not lie in the same diameter ; their positions are regulated by the direction of greatest magnetic intensity. Since the needle is vertical at both poles, the line of force seems to lie through the centre of the earth ; probably because there is there the greatest degree of polarisation. In one respect the irregularities of the magnetic needle are much less than might be expected. The magnetised substance being the atmosphere, it might be supposed that the direction of the needle would vary with every breath of wind, and in a storm would be tossed in every conceiv- able direction. This, however, is not the case. The needle is not affected by the most violent gale, if only it is protected from the mechanical effect of the storm. From magnetic pole to magnetic pole the atmosphere forms a semi-circular horseshoe magnet, and the magnetic force of every monad along that distance is exhibited at the positive and negative poles. The total magnetic force is therefore the same, both in direction and intensity, whether the atmosphere is at rest or in motion. Terrestrial Magnetism. 185 Magnetic force is materially affected by the motion of a magnetic substance between the poles of the magnet ; because, the medium being non-magnetic, the force is dispersed according to the square of the distance. Within the magnet there is no such dispersion, for every contiguous particle is paramagnetic, and the whole force acts along polarised lines. Thus, the well known fact that a magne- tised needle is not disturbed by ordinary storms, is not at variance with the view, that the atmosphere, and not the earth, is the seat of terrestrial magnetic force. CHAPTER VII. ATMOSPHERIC ELECTRICITY. 1. The Atmosphere an Electrical Machine. T^HE atmosphere possesses all the requisites of an electrical -L machine. The magnetised oxygen forms the field of force, the air in a moist state is a good conductor, and in a dry state is almost a perfect insulator. Under proper conditions all that is further required to produce electricity is motive power to pass the conductor through the lines of force. This cannot be done by the motion of the earth, either in its orbit or on its axis, because these motions are common to both the magnetic lines and the moisture of the atmosphere. The necessary power, however, is supplied by the wind, which causes transverse motion. It might be supposed that the motion produced by the wind would also be common to both conductor and lines of force, because the moisture of the atmosphere moves in common with the magnetised air. But the lines of force do not move with the air. The magnetic needle remains steady in the midst of a storm, showing that the lines of force pass through the moving atmosphere, and therefore through the moisture also which is contained in it. Magnetic force is a circuit from (magnetic) pole to pole, and is not interrupted by any local disturbances. Through AtnnospJieric Electricity. 187 that circuit the moist atmosphere is carried by the wind, and electric force generated on the same principle as that of a common dj^namo. Thus, the atmosphere is not only a complete electrical machine, but is also provided with the requisite motive power for working it. Electric power depends upon the strength of the magnetic field, the quantity of conductive matter passing through it, and ,the velocity of the motion. All these conditions are favourable for the production of strong electric force in polar regions. The magnetic intensity is about 2|- times greater than at the equator; on account of the extreme cold the atmosphere is very dense, and the northward flow of heated air in the upper region of the atmosphere causes a steady southward current of denser air along the earth's surface. To these combined causes we have to trace the appearance of the aurora borealis, or, more correctly, the av/rora polaris ; for the phenomenon is common to both polar regions. An intimate connection between terrestrial magnetism and the auroral phenomena is generally admitted. The nature of that connection appears to be, that the magnetic lines are the means by which the electricity which constitutes the aurora is produced. No other connection is known to science. There are some magnetic peculiarities within the polar circles which have, no doubt, a certain effect upon the electricity produced; for the electrical direction is always at right angles to the lines of magnetic force. But the aurora itself is not magnetic but electric. Magnetism is a form of cohesion and cannot be luminous. Among the particles of a magnetised substance there is no motion, which is an essential condition of light. Very little is yet known of the laws which regulate the manifold striking appeai'ances presented by the aurora, but they are 188 Molecular Forces and Xewtonian Laws. all discharges of electric force in some form or other, some of them resembling discharges through rarefied air. The polar regions possess the true electric light. 2. Electrical Direction. Electricity is generated at right angles to the lines of magnetic force. If the direction of the magnetic circuit is from the observer's right hand towards his left, and if the conductor passes through the magnetic lines in the direction of the observer, the electrical direction is towards his feet. If either the direction of the magnetic lines or the motion of the conductor be reversed, the current is towards the observer's head. By this rule we can tell generally the direction of atmospheric electricity, since we know the direction of terrestrial magnetism. In polar regions the lines of magnetic force are vertical, and therefore the electrical direction horizontal. In these circumstances it is hardly possible for insulation to take place. Both poles of the electric force being in the same stratum of the atmosphere, it is hardly conceivable that they could become insulated on all sides from one another by the intervention of a column of non-conductive air. This is probably the reason why in those regions the whole electric force is expended in producing the auroi-a, and thunder-storms are comparatively unknown. It seems to be a csise of strong electrification discharging itself through the intervening medium, in the same way as a strongly charged electrical machine produces brush-like discharges through the surrounding atmosphere. In lower latitudes, where the magnetic lines are more or less horizontal, the electrical direction is upwards or down- wards according to the direction of the wind. With an easterly or north-easterlj- wind, the atmosphere is electrified AtTiiospheric Mectncity. 189 positively towards the earth's surface, and with a westerly or south-westerly wind, negatively. It has been remarked that, with the exception of the wind, no natural phenomenon is so changeable as the electrification of the atmosphere near the earth's surface. The explanation appears to be, that it depends upon the direction of the wind. (See Note 27.) When the electrical direction is vertical, insulation will readily take place. When two banks of dense cloud are separated by a stratum of air with just sufficient moisture to form a conductor between them, with very little change in the condition of the atmosphere the intervening stratum may be converted into a non-conductor, and the two charged clouds become the poles of a static electric force. Thus, instead of being discharged in the form of an aurora, the electric force forms the nucleus of a thunder-storm. The earth is a much better conductor of electricity than vapour, and must be electrified, more or less, by contact with the electrified atmosphere. Or the electrified vapour contained in the atmosphere may distil and fall to the earth in the form of rain, when its surface will become electrified much more rapidly. An electric force is thus established between the earth and a cloud which may be at so great a height that, by the law of inverse squares, the force between them is almost imperceptible. But when the cloud is borne down to the earth's surface, the charge may prove to be of formidable power. Any number of such electric charges may exist simultaneously, having one of their poles in the earth and the other in a cloud of vapour far above it. If some have their positive and some their negative pole in the earth, it will make no difference. So long as the clouds are insulated from one another, the forces are all distinct, 190 Molecular Forces and Newtonian Laws. and any one of them may be discharged without inter- ference with the rest, just as any number of Leyden jars may have one of their coatings, positive or negative, connected with the earth, and any one of them can be discharged independently of all the others. This is probably the explanation of those sudden changes in the electrical condition of the earth's surface which are sometimes observed in the course of a thunder-storm. Before the discharge the earth's surface may be strongly positive, and after it as strongly negative. The discharge cannot of itself produce such an effect. At most it could only render the earth's surface neutral. But if there are more charges than one, and of different sign, the discharge of the positive may bring the negative into prominence. All these changes are in accordance with the known laws of electric force. 3. Eabth Currents. In working electric cables much trouble is caused to the electrical engineer by earth currents, which seem to be constantly passing everywhere through the earth and ocean. The origin of these currents is involved in obscurity. It is hardly possible that electric currents can be generated within the earth. Magnetic lines of force do, indeed, pass through the earth everywhere in the direction of the dipping needle, but there is no relative motion between these lines and any conductor, which is necessary for the production of electricity. Even if electricity could be generated on the thermo-electric principle, or on the chemical principle of the Galvanic battery, there could be neither a current through the earth, nor a static force, for want of the necessary insulation. The positive and negative elements of an electric force are generated at the Atmospheric Electricity. 191 same place and time ; and since the force between these elements or poles acts along the line of least resistance, there could be no current passing through the earth, which is everywhere conductive. The electric force would be instantly converted into heat at the point where it is generated. Moreover, such a source of electricity in the interior of the earth would be constant; but among the hidden treasures of the earth no one has ever discovered an electric mine ! There is the same obstacle to the formation of an electric current in the ocean. Lines of magnetic force pass also through the ocean, whose waters form a fairly good con- ductor. There is also a certain amount of motion for producing electricity; but there is no insulation. The electric force, if generated at all, would be instantly converted into heat locally, so that there could be neither a current nor a static force. The formation of currents being thus impossible in either the earth or the ocean, we seem to be shut up to the conclusion that earth currents are of atmospheric origin. The earth is the counterpart of the atmosphere in respect of electricity. We have seen that there may be any number of separate electric .forces, each having one of its poles in the atmosphere and the other in the earth. In the atmosphere the elements of the different forces are all insulated from one another; in the earth the poles of all the forces are combined in a single conductor. When the electrified cloud is carried along by the wind, the terrestrial element of the force accompanies it at the nearest part of the earth's surface. This force acting along the earth's surface will produce a current in any telegraph cable to which it finds access. It appears to be in this way that earth currents are produced. 192 Molecular Forces and Newtonian Laws. The force between the earth and the cloud is static, and there can be no discharge of the electric force until contact is established between the two poles. But the motion of the cloud produces a current without .any discharge : not with the same velocit}', but of the same nature as an ordinary current. And this appears to be characteristic of these earth currents. Interviewed with regard to the late magnetic storm, Mr. Gavey, the Electrician-in-Chief to the Post Office, said, " The earth currents do not go rapidly ; they move slowly in long, low curves, and we are able to use the condensers effectively." The velocity of earth currents is apparently that of the wind, by which they are produced. When an electric current is transmitted to a distance through an insulated cable, and the circuit completed through the earth, there is always a force tending to interrupt the current at any weak point in the insulation of the cable. But this is only the opposite pole of the force which is being operated with, and is not to be confounded with earth currents, which are of entirely different origin. 4. Magnetic Storms. Certain magnetic disturbances occur from time to time, causing great variations of the magnetic needle. At the same time there is an increased brilliancy of the auroral displays, and subsidiary currents are also set up in the common telegraph wires. Such disturbances are called magnetic storms. Another remarkable phenomenon frequently connected with these disturbances and which seems to indicate their cause, is the appearance of sun-spots. These are commonly supposed to be caused by the falling of Atmospheric Electricity. 193 great masses of meteoric matter into the body of the Sim. We know too little, however, of the action going on at the sun's surface to be sure of the nature of these spots; but this seems to be certain, that they indicate an accession to the intensity of the solar rays, especially of those rays upon which magnetisation depends. All the phenomena connected with magnetic storms can be accounted for by a sudden increase in the intensity of solar heat. Whatever the nature of sun-spots, they seem to denote a stirring up of the great furnace which gives light and heat to our solar system. (See Note 28.) The increased brilliance of the auroral phenomena is readily traced to this cause. Not only is the change observable in polar regions, but the aurora is also seen in much lower latitudes than in ordinary circumstances. This fact seems to indicate that the auroral phenomena are chiefly due to the intensity of the magnetic force in the polar regions ; for when that force is increased they appear at places more remote from the poles. However this may be, it seems certain that the magnetic storm in so far as it affects the aurora borealis, is due to a sudden increase in the magnetising force of the solar rays. The subsidiary currents set up in the telegraph wires can be traced to the same cause. The rays from an electric current produce a secondary current in an adjoining conductor, and such a momentary current is produced as often as the primary current, and consequently the heat rays from it, is increased or diminished in Strength. In ordinary circumstances the solar rays do not produce any • subsidiary current, or it is too feeble for observation. But when the magnetic force is increased by the greater intensity of the solar rays, a current is produced in the telegraph wires. N 194 Molecular Forces avd Newtonian Laws. That this is the true cause of these subsidiary currents is confirmed by the fact that they are most observable in wires running from the north-east to south-west, that direction being at right angles to the hnes of magnetic force, which at the present time are, in this hemisphere, from north-west to south-east. This order will, however, be reversed about 200 years hence ; for then the lines of force will be from north-east to south-west, and the wires most strongly affected will be from north-west to south- east. Any increase in the solar heat affects all magnetic phenomena in the same proportion, and consequently all the electric currents produced by means of the magnetic lines. The strength of the field of force being increased, the vapour of the atmosphere is more strongly electrified, and the earth currents established between the earth and the atmosphere acquire greater activity. Even where they are quite imperceptible in ordinary circumstances, they may seriously disturb telegraphic operations during the time of a magnetic storm. If further evidence were necessary to connect these magnetic phenomena with solar heat, it might be found in their wide-spread effects. These are felt simultaneously in all countries. During the recent magnetic storm, it is said that probably every magnetic needle in the world was affected. The eifects of a magnetic storm are felt wherever the solar rays fall. CHAPTER VIII. IDENTITY OF THE FORCES. 1. Matter and its Properties. MATTER is that which occupies space, and is therefore of three dimensions. All matter admits of contraction and expansion. Contraction is limited by contact, but expansion appears to be practically unlimited. The smallest quantity of matter may be expanded over almost any given space. Matter, like space, seems to possess endless divisibility. It is probable that atoms are only small masses which we have no means of subdividing. Contraction is caused by the force of attraction in accordance with the Newtonian law : expansion is caused by motion or energy. But all motion is generated by attraction. Motion may be transmitted from one body to another, but it is never originated except by contraction. From the shaft of the engine motion is transmitted to the lathes of the workshop, but it originates in contraction between the atoms of carbon and oxygen in the furnace. The solar rays transmit motion, but it originates in molecular attraction on the sun's surface. And motion, when expended, always produces expansion of the same mechanical value. This is Newton's law of action and reaction, now known as the conservation of energy. From this law it follows that all the kinetic energy of the universe must have originated in contraction, and it 196 Molecular Forces and Newtonian Laws. may be inferred that matter in its primary state consisted of a fine medium distributed evenly over unlimited space. In no other form could matter possessing attraction exist without motion. The origin of motion, like the origin of matter, lies behind the veil. (See Note 29.) Force is manifestly inherent in matter. The one is never separated from the other. Apart from matter, force is only an abstraction of the mind. The material universe may be regarded as a continuous system, co-extensive with space, and possessing an inherent power of contraction. But contraction produces motion, and motion implies a corresponding power of expansion. By this action and reaction, the evolution of the material universe is produced. All natural phenomena may be traced to interchanges of contraction and expansion, the total matter and energy of the universe remaining unchanged. And this law is applicable to organic as well as inorganic matter. Whatever the nature of life, it adds nothing either to the matter or to the energy of the universe. All the functions of organic bodies can be traced to action and reaction, the same as those of inorganic matter. The energy of the horse, like that of the steam-engine, originates in the consumption of fuel. (See Note 30.) Matter exists in dual form. The two elements of that duality are described as positive and negative ; but these terms convey no conception of the nature of the relation- ship. All we know is, that between the two elements there is a force of attraction. So far as known, every particle of matter has a positive and a negative point, and, between these, through the opposite points of all other particles, there is a force of attraction. This constitutes the self- contracting power of matter. The polarity of matter renders the force of attraction Identity of the Forces. 197 directive as well as convective. It tends not only to bring particles of matter into contact, but also to establish contact between opposite points. This does not always happen, because the particles are often held in rigid position by their combination with other particles, so that they cannot obey the directive couple. In these circumstances the force of attraction is much less than when the particles become polarised on contact. In the case of water, we have seen that the difference between the polarised and unpolarised force is equivalent to a difference of 80° C. in the temperature of the water. The same effect is observed in the crystallisation which takes place when the particles are brought into contact in favourable circumstances. They do not combine promiscuously, as they would do under a mere mechanical force, but arrange themselves in regular order according to their geometrical form. The difference of force is also shown by the great strength of the crystal in the direction of polarisation compared with the cleavage planes. The force of attraction presents itself to us in various forms, which have received distinctive names. The principal of these are gravitation, cohesion, chemical affinity, magnetism, and electricity. These are all so many modified forms of that one force of attraction which is inherent in all matter, and never changes. They can be all traced to the action of polarity, which produces different effects in different substances, or in the altered conditions of the same substance. The modifications which force thus undergoes will now be explained. 2. Gravitation. The force of attraction between two bodies is commonly called gravitation when there is a distance between them through which the force can produce motion. Thus, the 198 Molecular Forces and Newtonian Laws. force by which all bodies fall to the ground, or by which the various heavenly bodies move towards each other, is called gravitation. The term gravitation is also used when the two bodies are separated by a rigid substance so that no motion can take place. The force between the earth and a weight placed on the table, or between two balls on opposite sides of the earth, is gravitation. In all these cases the force of attraction acts by means of contiguous particles, in accordance with Faraday's law. If there were no material medium connecting the two bodies there could be no force of attraction between them. In pure physics, action at a distance is impossible. The material universe is therefore a continuous medium. The force of attraction between the earth and the remotest star shows that there is no break in the material system of the universe. By attraction through contiguous particles is meant that there is attraction between any given particle of matter and all other particles in contact with it, and again between these particles and all others in contact with them, &c. Thus, the number of the lines of force issuing from the given particle increases as the square of the distance from it. But force is inherent in matter, and cannot be expended. It is not affected, therefore, by the number of particles through which it acts, but only by the number of the lines into which it is sub-divided. This is the law of inverse squares ; for the number of the lines into which the force is divided is as the square of the distance from the particle, and therefore the force along any particular line is inversely as the square of the distance. This affords also an explanation of the fact that the force of gravitation between any two bodies is the same whether the intervening space is occupied by solid matter. Identity of the Forces. 199 01' by a rare medium such as the ether ; for the force is not affected by the number of particles through which it acts, but only by the distance. It is sometimes supposed that the force of attraction between the sun and moon is not affected during an eclipse of the latter body because the lines of force act through the earth by means of the ether. But ether and solid matter are alike in this respect ; both mean continuity of the material system, and the subdivision of the force into a number of lines increasing as the square of the distance. 3. Cohesion Cohesion is the force of attraction between particles of matter in contact. By the law of inverse squares the force increases up to the point of contact, and since force is inherent in matter and can never change, the particles are pressed together by that force at its maximum. From the nature of polarity, the force of cohesion is necessarily very different according as the particles combine with their opposite magnetic points in contact or not. If the particles are brought together in a rigid state, very few of them combine in the polarised form, and the cohesion is weak. If the particles come into contact in a state of solution or of fusion, they are free to move in accordance with the directive couple due to polarity; and, combining in the polarised form, the cohesion is strong. (See Note 31.) When two pieces of glass are brought together in a rough state there is no perceptible cohesion, the particles being too far apart. But if the two surfaces are very finely polished there is perceptible cohesion, because very many of the particles are brought into close contact. This is not due to atmospheric pressure, for the same effect is 200 Molecular Forces and Newtonian Laws. observed when the experiment is performed in a vacuum. Still the cohesion between the polished surfaces is very feeble, because there is little or no polarisation between the particles. But if the two pieces of glass are fused, so that the particles are free to move and become polarised when contact is made, strong cohesion is established between them. On this principle metals are welded, the contact of the particles being rendered more close by hammering. When particles of sand, dust, etc., fall upon the ground there is no cohesion among them ; but if they are subjected to strong pressure there is a certain amount of cohesion. The reason is obvious. The particles are brought so much nearer to each other, and attraction is increased according to the law of inverse squares. In this way stratified rocks are formed out of loose unconnected materials, by the pressure of superincumbent matter. In this case, however, the cohesion is generally increased by the per- colation of various substances into the interstices in a state of solution, where they polarise and give solidity to rock. The solidification of rocks appears to proceed also through course of time independently of the introduction of any extraneous matter. This seems to be promoted by the vibration among their particles due to temperature. Even an iceberg from the shores of Greenland, as it floats in the North Atlantic, is literally throbbing with heat, for its temperature is about 273° C. above absolute zero. Heat is a state of vibration, and facilitates molecular action among the particles of matter. It. seems to be due to this cause that metals, such as gold and lead, begin to inter-penetrate each other when left in contact for a great length of time. Such action could hardly Identity of the Forces. 201 take place if the particles were perfectly still. Some substances, such as water, whose particles are perfectly mobile, acquire their utmost cohesion instantaneously; others, whose particles come together in the solid state, acquire their highest degree of cohesion only after a great lapse of time. But in all cases the only force in operation is the attraction inherent in all matter. Cohesion is manifestly no more than a modification of the same force which, in other circumstances, we call gravitation. 4. Chemical Affinity". In all its essential features chemical affinity is identical with cohesion, of which it is a particular case. Cohesion forms masses, more or less compact, out of all material elements ; chemical affinity forms small compact masses, or molecules, out of the elements of some substances which combine in certain fixed proportions. The two outstanding features of chemical affinity are — the great heat produced in the process of combination, and the natural selection of elements entering into the combination. Some substances do not combine in this way at all; in other cases two substances may readily combine when alone, but when a third is added its atoms may combine with one of the former elements, to the rejection of the other. The elements thus make a kind of natural selection; they choose their partners, and fix the share which each shall have in the partnership. (See Note 32.) In all cases of chemical combination the particles must be free to move in accordance with their own inherent forces ; that is to say, the combining substances must be either in a state of fusion or in a state of solution. The heat of fusion can have no connection with the combination 202 Molecular Fmxes and Newtonian Laivs. of the particles, because it is a dispellent force. Neither can the water of solution cause the particles to combine, except in so far as its own elements may enter into the combination. The only force, therefore, which causes the particles to combine is that force of attraction inherent in the particles themselves. The elements, having perfect freedom of motion in the nascent state, combine in polarised form. The force being directive as well as convective, brings dissimilar points into contact. This is the explanation of the great heat of chemical combination. It has always been felt that the impact of the particles, under mechanical force, even allowing for the effect of inverse squares, is insufficient to account for the heat produced. The effect, however, is not due so much to the distance between the particles as to the polarisation. In the case of water, the particles are actually further apart in the polarised than in the unpolarised state, and yet the heat produced by polarisation is equivalent to a difference in temperature of 80° C. There can be no doubt that this is also the cause of the heat produced by chemical combination. The crystals of different substances assume different forms. From this it may be inferred that the atoms of which these crystals are composed are themselves geometrical figures of different forms, and that their magnetic points have a definite relation to their planes and angles. Some of these are adapted for closer contact than others, and form stronger combinations. It thus appears that the strength of a chemical combination does not depend upon the nature of the combining force, but upon the form of the combining particles. The force in all cases is the attraction inherent in the material particles, but the strength of the cohesion is regulated by their form. Identity of the Forces. 203 Attraction and heat are antagonistic forces; the one produces contraction, the other expansion. When the dispellent power of heat is greater than the cohesive force of attraction between the particles of any body, it becomes fused, and the particles are then free to move in accordance with their inherent forces. If A, B, C, be three substances composedrespectively of the atoms acta. . . . ,hhh . . . , ccc . . . , and, if the force of attraction between a and h is greater than between a a or bb, when A and B are fused a new substance, ababab . . . is formed, or molecules consisting of these atoms, in certain proportions, because the new combination resists a greater heat than the original substances. Again, if these molecules and the substance, C, be fused together, and if the force between b and c is greater than between ab or a c, a third sub- stance, bcbcbc . . . is formed, because it resists greater heat than the former combination, and the particles, aaa, remain in fusion. Now, this is natural selection, which only means the survival of the fittest. The particles whose combination resists the greatest heat are the elements of the new substance. If A,B, C in the above case be mercury, sulphur, and iron, the first combination ab, ab, ab . . . is vermilion, and the second combination be, be, 6c ... is sulphide of iron, the mercury being set free. Molecules, like atoms, have each a positive and a negative magnetic point, and follow the same law with respect to polarisation. It seems probable, therefore, that atoms are also combinations of smaller elements, but so strong that they defy all our efforts to subdivide them. They appear to be one of the earliest formations in the evolution of matter, and to have survived all the changes which it has undergone in the lapse of ages. 204 Molecular Forces and Newtonian Laws. From all these considerations there seems no reason to doubt that the force known as chemical affinity is only another form of that force of attraction which is inherent in all matter. The great heat of combination is accounted for by the Newtonian law of action and reaction, and the natural selection is the necessary effect of polarity. There is no need to speculate about another cause when one cause sufficient to account for the phenomena is known to exist. 5. Magnetism. Magnetism is a force of attraction which resides in the substance of the magnet. If this were not so, the force of any magnet would become exhausted in a short time by the production of energy. But the strength of a magnet remains unimpaired for any length of time, if only the particles are kept in the polarised state. Now, the only force which is known to reside in matter, and to undergo no change, is that force of attraction by which, according to the Newtonian law, every particle attracts every other particle. We conclude, therefore, that magnetism is a modification of that force. The force of attraction between any two monads is inversely as the square of the distance between their opposite magnetic points. But when a substance is polarised the opposite points of the monads are in contact, and therefore the force of attraction between them at its maximum. And this is the condition of a magnetised substance, as is shown by the direction of a magnetised needle when placed in magnetised air. All the positive points of the magnetised substance lie in one direction, and all the negative points in the other. Through a magnetised substance, therefore,the particles form polarised lines, and the force of attraction between particle and particle along these lines is at its maximum. Identity of the Forces. 205 The effect of polarisation upon most substances is to produce a state of rigid cohesion between the particles. In the case of water, for instance, it constitutes the difference between the liquid state and ice. In the case of iron and some other substances, however, the efPect of polarisation is to produce a force of attraction along the polarised lines, so that the positive element of all the monads along any line is exhibited at one extremity of the substance, and the negative element of all the monads at the other. In this condition the whole substance forms a single monad, having one positive and one negative pole, and these equal in amount to the combined positive and negative elements of all the monads forming the polarised lines. There is, therefore, no diminution of the force by distance through the magnet; that is to say, the force is not distributed over a wider area by radiation, but is restricted to the polarised lines. This accounts for the great strength of magnetic force compared with ordinary gravitation. And it is in strict accordance with the Newtonian law ; for although the distance between the particles along the magnet is not reduced, the length of the magnet does not count for distance inasmuch as the elements of force are exhibited at its extremities. The action of magnetic force is also the same as that of ordinary gravitation. It causes motion of (magnetic) particles from any distance up to the point of contact and then holds them together in a state of cohesion. No further motion can take place until the particles are again separated by kinetic energy. This is the law of ordinary gravitation. The length of a magnetised body is only a point in respect of magnetic force. In a magnetic circuit the distance is therefore diminished by the combined lengths of all magnetic substances contained in it. Hence 206 Molecular Forces and Neivtonian Laws. the great force of magnetism, like ordinary gravitation, is clue to the law of inverse squares. Through non-magnetic matter the force radiates in all directions, and there is no diminution of the distance between monad and monad. For this reason there is no magnetic attraction between a magnet and a non-magnetic substance. It thus appears that all the phenomena of magnetism are accounted for by the ordinary force of attraction acting in accordance with ascertained laws. If it be maintained that magnetism is something distinct from ordinary attraction, it must be assumed that there is another force also inherent in matter, and exhibited only in the polarised state of any substance, and following in all respects the same laws as gravitational force; But such an hypothesis is too unreasonable to be seriously entertained. Magnetism isobviouslyamodified form of gravitational force. The magnet is said to have first suggested to Democritus the idea of terrestrial gravitation. Although he did not understand the nature of the magnet and its relation to gravitational force, he was right in principle. Magnetism is only modified gravitation. The late Dr. Tyndall also recognised the identity of gravitation with magnetism and chemical affinity, but he was under the impression that magnetism has somehow an element of repulsion connected with it. He had unfortunately accepted without due investigation, the common theory of magnetic repulsion, otherwise he would have confirmed the view of Democritus that magnetism and gravitation are only different forms of the same force. 6. Electricity. Faraday was of opinion that electricity is closely allied to chemical affinity, and this view seems to be correct. Identity of the Forces. 207 The force which causes the combination of the atoms forming a molecule is that attraction which is inherent in matter ; and the great strength of the cohesion is due to polarisation ; that is, to contact between dissimilar points of the atoms. If we had the means of slightly separating the atoms of a molecule and again allowing them to combine, the action would be very similar to that of an electric current. Work would be necessary to produce the separations, and heat would be produced by the contacts. The action of an electric current is also twofold. The magnetic points of the atoms are polarised and slightly separated by work performed by means of polarised lines of force, and again allowed to combine, or at least to approach each other, by the force of attraction in its polarised form. When the magnetic points are separated, they are in a state of potential energy, and the body is said to be electrified. When the force of attraction acts through the distance thus produced, the work is again converted into heat, and this process is called an electrical discharge. The term, electricity, is properly applicable to the combining force only, and is therefore a form of attraction. It may be observed that electric force is directive rather than convective. It does not seem to affect the distance between the particles of the substance, but only the distance between their magnetic points. The electrifying power is work done by means of polarised lines of force. That force acts upon the opposite extremities of a particle, and is, therefore, a directive couple. Under the influence of such a force the conductor is polarised. The particles are placed in the same direction, but not separated from one another. Discharge is in the opposite direction, 208 Molecular Forces and Newtonian Laws. and, therefore, directive also. It is action of the same kind as that which produces the great heat of chemical combination. The collision of polarised particles, whether in a crucible or in an electric current, produces great heat ; but a good conductor, such as silver or copper, is very little heated bj' the passage through it of an electric current. It seems probable, therefore, that the motion of the particles in an electric current does not consist of alternate contacts and separations as in ordinary heat, but vibrations, like those of a pendulum, the motion from one extremit}' of the vibration to the centre being due to the electric force, and from the centre to the other extremity to the work done by means of polarised lines of force. These vibrations are much longer and less rapid than ordinary heat vibrations, but they are of sufficient rapidity to produce etheric waves, like ordinary heat vibrations. These waves possess great penetrative power, and magnetise any paramagnetic substance which passes through them transversely with great velocity. In speaking of an electric current, it is necessary to distinguish carefully between the force by which the opposite points of the particles are brought towards each other, and that by which they are separated. To the first only the term electricity is applicable; the separating power is a form of kinetic energy, and is the very opposite of electricity, In both electricity and chemical affinity the contractive power is polarised attraction, which, as we have seen, is only a particular form of that force which is inherent in all material particles. Electricity is therefore a modified form of that same force which in other circum- stances we call gravitation. Identity of the Forces. 209 7. How Force Operates. Nothing is yet known of the cause of attraction between the particles of matter, but we can trace the modus operandi of that force. (See Note 33.) All matter, as we know it, consists of monads, each of which has a positive and a negative pole or point. Between these magnetic points there is a force of attraction which acts through contiguous particles, and is a constant quantity. Hence every particle of matter attracts every other particle, and the total force of the universe is constant. Since force exists only between dissimilar points, every line of force between the extremities of a monad forms a complete circuit which has a positive and a negative direction. The positive direction is from the positive point of the monad through adjacent particles to the negative point, and the negative direction from the negative point of the monad through adjacent particles to the positive point. There are not two forces, but a positive and a negative element of attraction, both of which are necessary to constitute force. When the length of the monads is an infinitesimal quantity in respect of the distance between them, the circuits are straight lines. Force in this form is called gravitation, and hence the Newtonian law that every particle of matter attracts every other particle, and that the direction of the force is in a straight line between them. Force being a property of matter cannot vary so long as the constitution of matter remains unchanged. For this reason the force between the extremities of a monad is the same at any distance from the monad. The force acts through contiguous particles, and is distributed over a greater area the greater the distance. But the total force 210 Molecular Forces and Newtonian Laws. is a constant quantity and is, therefore, the same foi- every particle at the surface of any sphere of which the monad is the centre. Hence from the nature of a sphere, the force of attraction between any two particles is inversely as the square of the distance between them. This law may be illustrated by the rings formed on the surface of a pool when a stone is dropped into the water. The rings increase in length according to their distance from the centre, but each represents the same amount of energy as that which preceded it, except for loss by friction. And since the circumference of a circle is in proportion to the radius, the energy at any point in one of the circular waves is inversely as the distance from the point where the stone fell into the water. In the case of force there is no loss by friction, neither is it expended by producing motion. The distance through which it can act, and therefore the potential energy of the force, is diminished by motion, but force is a property of matter and is not subject to increase or diminution. Through unpolarised matter, the force of attraction between the poles of a monad is subdivided into a greater number of lines of less intensity according to distance, but the sum of all these lines is the same at any distance whatever. When some substances are polarised the force of the monads does not radiate equally in all directions, but is restricted to the polarised lines. Force acting in this way is called magnetism. That part of the force which is polarised is uniform throughout the whole length of the magnetised substance, whereas it radiates equally in all directions through unpolarised matter. Hence Faraday's terms, paramagnetic and diamagnetic, for the two classes of substances. Identity of the Forces. 211 The force of attraction is neither increased nor diminished by magnetisation. If any monad be taken in the interior of an unmagnetised bar of iron, the force between the poles of the monad radiates in all directions, and is the same at every point in the surface of a sphere of which the monad is the centre. If the iron be magnetised, the the equipotential distance is the surface of an ellipsoid of which the poles of the magnet are the foci. The positive and negative elements of the monad, in so far as polarised, are exhibited at the poles of the magnet ; and when these are brought into contact, we have the remarkable phenomenon of opposite magnetic points of the same monads in contact, without any radiation through contiguous particles. Hence the great force between two magnetic poles when they are connected by a keeper. (See Note 34.) The total force of a magnet is made up of two components. One of these, which may be called a, is the force between the particles of the magnet; the other, which may be called x, is the force of gravitation. Between every particle of the earth and every particle of the magnet there is a force of attraction, and that force through the magnet necessarily follows the polarised lines. If/ be the total force of the magnet, /= a + x. Now, a is constant, because the force between the particles of the magnet is the same in all positions. But x is variable, because gravitation diminishes according to distance from the centre of the earth. A magnet should sustain a slightly greater weight at the equator than at London ; but tested by means of a spring it should be a little weaker at the equator. When the length of any two monads is a negligible quantity in respect of the distance between them, the 212 Molecular Forces and Newtonian Laws. direction of the force is a straight line, and of this nature is all gravitational force. But all motion is due to force, and is therefore in the same direction. In virtue of inertia, particles set in motion by force are carried to the same distance past each other, if they do not collide. All motion produced by gravitation is therefore vibratory, with an interchange of potential and kinetic energy at the centre of the vibration. When a gun is fired, the recoil of the gun is exactly equal to the vis viva of the ball ; and, if undisturbed, both would return to the same point and with the same energy. This never happens ; but the dis- turbing cause acts according to the same law, so that the motion is a compound vibration. When the particles collide, the motion is of the same nature, but the vibrations are shorter and more rapid. Motion in a circuib, such as the orbit of a planet round the sun, is a compound vibration; for if a line be drawn from any point in the orbit through the centre of gravity of the two bodies to the opposite side of the orbit, the motion in the direction of that line is a vibration with an interchange of potential and kinetic energy at the centre of gravity. Motion in any circuit whatever, is a compound of many vibrations. (See Note 35.) From the above law it follows that all matter is in a state of vibration. When the vibrations are very short and very rapid the motion is called heat ; but it is motion of the same kind, and governed by the same laws, as the revolution of the heavenly bodies round each other. The temperature of matter without any motion among its particles would be absolute zero ; but it is probable that no such matter exists in the present state of the universe. When the length of the monads is an appreciable quantity in respect of the distance between them, the Identity of the Forces. 213 force of attraction forms a directive couple which tends to bring the dissimilar points into contact. The effect of the directive couple is to produce crystallisation when particles combine under circumstances favourable for its operation. Heat, being a state of motion among the particles of a body, prevents crystallisation ; when, therefore, any substance is in a state of fusion, crystallisation can take place only under a falling temperature. The evaporation of a liquid reduces temperature, or absorbs heat — to use the common expression — ^and is, therefore, favourable for the crystallisation of substances in a state of solution. The different forms of crystals are manifestly due to the different forms of the atoms of which they are composed. If we knew the forms of the atoms, and the relation of the magnetic points to their planes and angles, to tell the forms of the crystals would only be a problem in solid geometry. It is probable that the primary monads were of infinitesimal dimensions, and that material atoms were formed by different combinations of these. This would account for the different geometrical forms of atoms, and the process may have constituted a former stage in the evolution of the material universe. There is no difference between organic and inorganic matter in so far as force and motion are concerned. All the phenomena of animal and vegetable physiology, in so far as these are understood, can be reduced to the operation of the same laws which regulate the phenomena of inorganic matter. The molecules of which organic bodies are constituted are only combinations of inorganic substances. These combinations are formed according to the laws of inorganic matter, and the molecules after formation are still regulated' by the same laws; just 214 Molecular Forces and Newtonian Laws. as the molecules of water, though differing in many respects from the elements of oxygen and hydrogen, are regulated by the same laws of force and motion. (See Note 36.) Many physiological phenomena are as yet only imper- fectly understood ; but the fact that, in so far as their nature has been clearly ascertained, they conform to the Newtonian laws, leaves little reason to doubt that the rule is universal. Any physical phenomenon that cannot be squared with the Newtonian laws of force and motion, is something of which our knowledge is still imperfect. EXPLANATORY NOTES. Note 1, page 16. " I have long held an* opinion, almost amounting to con- viction, in common, I believe, with many other lovers of natural knowledge, that the various forms under which the forces of matter are made manifest have one common origin ; or, in other words, are so directly related and mutually dependent, that they are convertible, as it were, into one another, and possess equivalents of power in their action. In modern times the proofs of their convertibility have been accumulated to a very considerable extent, and a commence- ment made of the determination of their equivalent forces." — (Faraday's Experimental JResearches in Electricity, Art. 2146.) There seems good reason to believe that all force is, in its nature, essentially one ; and it only remains to define more clearly than has yet been done the various modifications which it undergoes. This, the design of the present work, is there- fore in accordance with the general trend of opinion among the best authorities on the subject. Note 2, page 17. Attraction is a well established law of matter ; repulsion is only an hypothesis. Since attraction draws all particles of matter towards each other, and yet all bodies in the gaseous state are compressible, there must be some power by which the particles are kept apart The true nature of that repellent power appears to have been first pointed out by Sir Humphry Davy, who says, " The particles of bodies may be considered as acted on by two opposite forces, the approximating power which may (for greater ease of expression) be called attraction, and the repulsive, motion. The first of these is the compound 216 Molecular Forces and Newtonian Laws. efifect of the attraction of cohesion, by which the particles tend to come in contact with each other, the attraction of gravitation, by which they tend to approximate to the great contiguous masses of matter, and the pressure under which they exist, dependent on the gravitation of the superincumbent masses. The second is the eiFect of a peculiar motory or vibratory impulse given to them, tending to remove them farther from each other, and which can be generated, or rather increased, by friction or percussion. The effect of the attraction of cohesion, the great approximating cause, on the corpuscles of bodies, is exactly similar to that of the attraction of gravitation on the great masses of matter composing the universe, and the repulsive motion is analogous to the planetary projectile force." — {Works, vol. ii., page 15.) It will be observed that Davy speaks of " repulsive motion,'' not of repulsive force. He considered the great expansive power of nature to be motion. Referring to this view. Lord Kelvin says, " Here we have a most important idea. It would be a somewhat bold figure of speech to say that the earth and moon are kept apart by a repulsive motion, and yet after all, what is centrifugal force but a repulsive motion 1 and may it not be that there is no such thing as repulsion, and that it is solely by inertia that what seems to be repulsion is produced 1 " — (Popular Lectures and Addresses, vol. i., page 222.) Again (page 224), Lord Kelvin says, "Joule, Clausius, and Maxwell, and no doubt Daniel Bernoulli himself, and I believe every one who has hitherto written or done anything very explicit in the kinetic theory of gases, has taken the mutual action of molecules in collision as repulsive. May it not after all be attraction 1 " Note 3, page 19. The equation /rf= ^^ is easily established algebraically. Since the force of attraction is in proportion to the mass,/ = HI. If g be the velocity acquired in one unit of time, the Explanatory Notes. 217 velocity acquired in t units is g t, that is, v = g t, and therefore V t = -• At the beginning of the first unit of time the body has no velocity, and at the end of the first unit it has a velocity (/ ; therefore the distance moved in the first unit of time is g, and by the law of inertia the distance moved in the time t is -g-, that is, d = '-n- Substituting for t the value given above, we get c? = 27 J ^'Hd since/=m,/af= -jj— . Note 4, page 21. " What is meant, in the case of chemical affinity, is, that the pull of that afiLnity, acting through a certain space, imparts a motion of translation of one atom towards another. This motion is not heat, nor is the force that produces it heat. But when the atoms strike and recoil, the motion of translation is converted into a motion of vibration, which is heat. The vibration, however, so far from causing the extinction of the original attraction, is in part carried on by that attraction. The atoms recoil, in virtue of the elastic force which opposes actual contact, and in the recoil they are driven too far back. The original attraction then triumphs over the force of recoil, and urges the atoms once more together. Thus, like a pendu- lum, they oscillate until their motion is imparted to the surrounding ether; or, in other words, until their heat becomes radiant heat." — (Tyndall's Fragments of Science, vol. i., page 9.) Note 5, page 22. " Latent heat " is a contradiction in terms. Heat is motion, and latent heat would mean motionless motion. It is now generally admitted that the expansive power of a gas is due to molecular motion among its particles, and if that motion were to cease the gas would liquify. In like manner the liquid 218 Molecular Forces and Newtonian Laws. state of any substance is due to molecular motion among its particles, and if that motion were to cease the Hquid would solidify. Heat is therefore in its active form in the gaseous and liquid states of any substance, the same as in the solid state. But the heat of a gas at the liquifying point, or of a liquid at the freezing point, cannot be communicated to another substance, such as the bulb of a thermometer, without producing condensation ; and in the process of condensation a corresponding amount of heat is produced, so that there is no change in temperature until the whole of the gas is converted into the liquid state, or the whole of the liquid into the solid state. Hence the erroneous idea that in these cases the heat is latent. Note 6, page 26. " In searching for some principle on which our experimental inquiry after the identification or relation of the two forces (electricity and gravity) could be founded, it seemed that if such a relation existed, there must be something in gravity which would correspond to the dual or antithetical nature of the forms of force in electricity and magnetism." — (Faraday's Experimented Researches in Electricity, Art. 2703.) The duality which Faraday desiderated in gravity, in order to identify it with electricity and magnetism, is found in the polarity of all matter ; and it will be shown hereafter that the law of magnetism, when the size of the magnets is infinitesimal, is the law of gravitation. Note 7, page 26. "For anything we know to the contrary, gravitation and cohesion may be mere modifications of the same general power of attraction, in the one case acting at distances which can be easily measured ; and in the other case, operating at distances which it is difficult to estimate." — (Davy's Works, vol. iv., page 17.) Explanatory Notes. 219 "It is satisfactory to find that, so far as cohesion is con- cerned, no other force than that of gravitation need be assumed." — (Kelvin's Popula/r Lectures amd Addresses, vol. i., page 63.) Note 8, page 27. Elasticity is the property which some bodies possess of retaining their shape. "Whether the body is compressed or distended, the force of attraction among its particles, within certain limits, restores it to the same form as before. When a slip of steel is bent into a semi-circular form, the particles on the convex side are distended and the particles on the con- cave side compressed. The force of attraction among these particles restores the metal to its original form. It thus appears that the resilience of the spring consists in a state of potential energy into which the particles are put by the dis- turbing force, and that potential energy is converted into kinetic energy when the disturbing cause is removed. Sometimes the kinetic theory of gases is accounted for by the perfect elasticity of the particles. The separation of the particles in that case, however, is not due to their elasticity but to " repulsive motion," to use Sir Humphry Davy's expression. And the expansive power of the gas is the same whether the particles collide or move round one another in orbits, just as the centrifugal force of the earth is the same whether it moves in an orbit round the sun or collides with that body ; only in the one case the energy is mechanical and in the other molecular. It is also matter of indifference whether the particles are elastic or inelastic, as pointed out by Lord Kelvin, who says, " Though each particle have absolutely perfect elasticity, the end must be very much the same as if it were but imperfectly elastic. The average eifect of repeated and repeated collisions must be to gradually convert all the translational energy into energy of shriller and shriller vibra- tions of the molecule." — {Popular Lectwres and Addresses, vol. i., page 230.) 220 Molecular Forces and NewtonioAi Laws. Note 9, page 35. "The very last time I saw him (Faraday) at work in the Royal Institution was in an underground cellar, which he had chosen for freedom from disturbance ; and he was arranging experiments to test the time of propagation of magnetic force from an electro-magnet through a distance of many yards of air to a fine steel needle polished to reflect light ; but no result came from these experiments." — (Kelvin's Popula/r Lectures and Addresses, vol. ii., page 541.) These experiments of Fara- day's yielded no result, because he was seeking what has no existence in nature — a relation between force and time. Force can exist only between two material points, and therefore extends over the whole distance between them. In the " tug of war " there can be no strain at any point in the cable unless it exists at every point. The strain does not move along the cable in time. All motion occupies time, because the moving body cannot occupy two positions at the same time. The force of attraction between the earth and sun has no relation to time, but any motion of the earth in its orbit occupies time. Electricity is a force of attraction, and has no relation to time ; but the transmission of a message from one station to another implies motion among the particles of the conductor, and therefore takes place in time. Note 10, page 39. It might be supposed that chemical affinity is an exception to the mechanical law that the product of the force into the distance through which it acts is equal to the energy produced. When, for instance, water and sulphuric acid are mixed together, great heat is produced, and yet the distance through which the particles move is practically nil, because there is no perceptible difference in the volume of the two liquids in the separate and combined states. The explanation is, that in this case the motion is not one of translation but of gyration. Explanatory Notes. 221 If two magnets be suspended by their respective centres of gravity and placed with their similar poles in contact, when allowed to move freely they turn round tUl their dissimilar poles come into contact. Bj- that motion considerable energy is produced, and yet the two magnets are not nearer to one another than when their similar poles were in contact. In the case of water a large amount of heat is produced in the process of freezing, although the particles are actually farther apart in the frozen than in the liquid state. The action is apparently similar to that of the two magnets. The energy required to place the magnets with their similar poles in contact, corre- sponds with the heat that is necessary to dissolve the ice ; and the energy produced by the contact of the dissimilar poles corresponds with the heat produced when the water freezes. This seems to be the law of chemical affinity. The great heat produced by combination is due, not to a motion of translation but of gyration. It forms no exception, therefore, to the Newtonian law of action and reaction. Note 11, page 40. " I cannot discover that any contemporary physicist or chemist believes in the real indivisibility of atoms, or in an interatomic matterless vacuum. The term ' atoms ' appears to be used as a mere name for physico-chemical units which have not yet been subdivided, and ' molecules ' for physico-chemical units which are aggregates of the former."— (Huxley's Collected Essays, vol. i., page 75.) Note 12, page 42. " Oxygen appears to be a very magnetic substance, for it passes axially, or from weaker to stronger places of force, with considerable power ; a conclusion in accordance with the result of former observations. Moreover, it passes more powerfully when dense than when rare, its tendency inwards being apparently in proportion to its density. Hence, as the oxygen 222 Molecular Forces and Newtonian Laws. is removed, the magnetic force disappears with it, until when a vacuum is obtained, Uttle or no trace of attraction or inward force remains." — (Faraday's Experimental Researohen in Electricity, Art. 2782.) XoTE 13, page 44. "There are strong reasons for believing that the art of magnetising iron or steel does not consist in imparting magnetisation to the molecules of which it is composed, but that these molecules are already magnetic, even in unmagnetised iron, but with their axes placed indifferently in all directions, and that the act of magnetisation consists in turning the molecules so that their axes are either rendered all parallel to one direction, or at least are deflected towards that direction.'' — (Maxwell's Electricity and Magnetism, Art. 832.) ZSToTE 14, page 45. It is universally agreed that magnetism is a force of attraction; the only oubstanding problem is with regard to the origin of that force. Franklin ascribed it to a magnetic fluid. He supposed that a substance is positively magnetised when it is super-saturated with the fluid, and negatively when drained of it. This hypothesis is now almost unanimously rejected, but the terminology of magnetic science is based upon it, and is therefore misleading. Among present-day authorities, Professor Sir Oliver Lodge supposes magnetism to be rotation in " an infinite ocean of incompressible and inexpansible, all-permeating perfect liquid." This theory resolves magnetism into a mode of motion. But motion, as we have seen, is repulsive, and magnetism is admittedly a force of attraction. The view of Lord Kelvin is expressed in the following passage : — " It will often be convenient to refer the phenomena of magnetic force to attractions or repulsions mutually exerted between portions of an imaginary magnetic matter, which, as we shall see, may Explanatory Notes. 223 be conceived to represent the polarity of a magnet of any kind. This imaginary substance possesses none of the primary qualities of ordinary matter, and it would be wrong to call it either a solid, or the ' magnetic fluid,' or ' fluids ' ; but, without making any hypothesis whatever, we may call it ' magnetic matter,' on the understanding that it possesses only the property of attracting or repelling magnets or other portions of ' matter ' of its own kind, according to certain determinate laws." — {Electrostatics and Alagnetism, Art. 463.) Lord Kelvin does not formulate any hypothesis, but only suggests " magnetic matter " as a means of fixing the idea in thinking and speaking of something, the nature of which is unknown. The effect, however, appears to be the opposite of what Lord Kelvin contemplated. A magnetic fluid, vortices in an ocean of incompressible liquid, magnetic matter possessing none of the primary qualities of ordinary matter, electric currents flowing round the atoms of a solid, homo- geneous substance, are so many flights of scientific imagination, and tend to distract the mind from the true nature of magnetism — a modification of that force of attraction which belongs to all matter. Note 15, page 53. The nature of a magnetic circuit was proved experimentally by Faraday, who says, " So, by this test there exist lines of force within the magnet, of the same nature as those without. What is more, they are exactly equal in amount to those with- out. They have a relation in direction to those without ; and, in fact, are continuations of them, absolutely unchanged in their nature, so far as the experimental test can be applied to them. Every line of force, therefore, at whatever distance it may be taken from the magnet, must be considered as a closed circuit, passing in some part of it through the magnet, and having an equal amount of force at every part of its course." /Experimental Researches in Electricity, Art. 3117.) 224 Molecular F&ives and Newtonian Laws. Note 16, page 57. Let A B C be any triangle, and A D a line bisecting^the angle BAG. Also^ let SPN be a Une at right angles to A D, and S' P N' the same line in any other position. Join BS' and ON'. It is required to prove that BS' + CN' is greater than B S + ON. Join A S' and AN'. The line A P bisects S N, the base of the triangle , SAN, and also B D C S' N' the base of the triangle S' A N' ; and since A P S is a right angle and APS' less than a right angle, A S and A N are equal, and A S', A N' unequal. The squares on the four sides of a parallelogram are equal to the squares on the diagonals, and the squares on any two adjacent sides to half the squares on the diagonals ; therefore the squares on S A and A N are equal to the squares on S' A and A N'. By Eu. II., 9, there- fore, S A + A N is greater than S' A + A N'. But B S' + S' A is greater than B A, and CN' + N'A is greater than CA. Still more, therefore, is B S' + C N' greater than B S + C N. Note 17, page 72. '■ The modern theory of electricity, generally known as the molecular or mechanical theory, considers the phenomena which we have classed under the head of electricity as being due to motion in the molecules of matter, similar in kind, but differing perhaps in direction, in amplitude, and rapidity to those which we know as sound, heat, and light." — (S. R. Bottone's Electricity am,d Magnetism, page 86.) Explanatory Notes. 225 This mechanical theory of electricity is a distinct departure from the material theory ; but it is not correct to speak of electricity as a mode of motion like sound, heat, or light. Electricity is not motion, tut force which causes motion. Note 18, page 83. The incongruity involved in the assumption of a gradual fall of potential along the course of an electric current, while the power of the current is the same at every point in the circuit, is shown by the following passage from Professor Everett's edition of Deschanel : — " When a steady current is flowing through a galvanic circuit, there must be a gradual fall of potential in every uniform conductor which forms part of the circuit, since in such a conductor, the direction of a current must necessarily be from higher to lower potential. These gradual falls are exactly compensated by the abrupt rises (diminished by the abrupt falls, if any) which occur at the various places of contact of dissimilar substances. Recent experiments by Sir W. Thomson seem to prove that by far the most important of these abrupt transitions occur at the junctions of dissimilar metals, a view which was originally propounded by Volta, who appears, however, to have over- looked the essential part played by chemical combination in supplying the necessary energy." — {Deschanel, Art. 740.) The current receives an accession of potential at every pair of plates in the battery, but the strength of the current is uniform along the conductors between the different pairs, and between the terminals which connect all the pairs. How, then, is the strength of the current maintained along these conductors % It would necessarily diminish with a fall of potential ; and there are neither junctions of dissimilar metals nor chemical combinations to maintain the potential, because the conductors are homogeneous and their chemical condition is not altered by the passage of the current through them. The fundamental error lies in thinking of electricity as P 226 Molecular Forces annd Newtonian Laws. something that moves, whereas it is a force which causes motion of the particles of the conductor. And, since the positive and negative elements of that force are at the opposite extremities of the conductor, the force is of uniform potential throughout its whole length. Note 19, page 88. The law by which force varies in intensity according to the area over which it is distributed, was observed, in connection with electrical phenomena, by Hertz, who writes as follows : — " On studying the experiments above described, the mode in which we have interpreted them, and the explanations of the investigators referred to in the introduction, one diflference will be found especially striking between the conception here advocated and the usually accepted view. In the latter, conductors appear as the only bodies which take part in the propagation of electrical disturbances, non-conductors as bodies which oppose this propagation. According to our conception, on the other hand, all propagation of electrical disturbances takes place through non-conductors ; and conductors oppose this propagation with a resistance which, in the case of rapid alternations, is insuperable. We might almost feel inclined to agree to the statement that con- ductors and non-conductors should, according to this conception, have their names interchanged. Such a paradox, however, only arises because we omit to specify what conduction or non- conduction is under discussion. Undoubtedly metals are non- conductors for electric force, and for this very reason they, under certain conditions, restrain it from becoming dissipated, and compel it to remain concentrated ; they thus become con- ductors of the apparent source of these forces — the electricity — to which the usual terminology has reference." — {Electric Waves, page 171.) Hertz had not observed the distinction between electric force, properly so called, and the kinetic energy produced by Explanatory Notes. 227 and the force along P S is The resultant of these forces that force. He speaks of both as electricity, and consequently certain obscurity runs through his description. But he dis- tinctly recognised the fact that within a conductor the force is concentrated within narrow limits, whereas, through a non- conductor, it becomes distributed over a wide area. Note 20, page 88. Let N S be two electric poles, and P any point in space. Join P N and P S, and let these distances be called a and 6 respectively. The force along PN is j_ a?' \ 62- lies somewhere within the angle N P S. Let P P' be the direction of the resultant, making an angle A with P I^, and an angle B with P S, and let f be the resultant force along P P'. From N draw N C at right angles to P P', and produce to meet PS, or PS pro- duced, in the point M. Prom N and M draw N P' and M P', parallel respectively to P M and P N. Also draw Q P Q' parallel to N M. The force -g may be resolved into two components, —^ sin -A- along P Q, and — g cos A along P P'. Also the force p may be resolved into p sin B along PQ', and p cos B along PP'. Now, —2 sin -A. = p sin B, because they are in opposite direc- tions and do not move the point P. Also -^ sin A = N C, and p sin B = C M ; therefore N C'= C M, and the line P P' bisects the angle N P S. But it is a property of an ellipse, that the 228 MolecvXar Forces and Newtonian Laws. bisector of the angle between the focal distances is normal to the circumference ; therefore the force / is normal to the circumference of an ellipse, or to the surface of an ellipsoid, of which N and S are the foci. Again, /= -\ cos A + p cos B ; or if the whole angle N P S be called P,/= (^j + p) cos ^. The force/ is not affected by any variation of a and h, so long as a + h is a constant quantity, because — , cos -g- = p cos -^. But it is a property of an ellipse that the sum of the focal distances from any point in the circumference is a constant quantity. The surface of an ellipsoid is, therefore, an equipotential area, and it has been shown that the force is normal to the surface. When the distance between N and S vanishes, the ellipsoid p merges into a sphere; also a = h, and cos -2^ = 1- The force, therefore, at every point on the surface of the sphere is -5 . This is the law of gravitation, which differs from magne- tism only by the length of the monads. It is correctly repre- sented as the resultant of two equal and parallel forces, because every force is a complete circuit between the positive and negative points of a monad. The force is inversely as the square of the distance, because the equipotential area is the surface of a sphere of which the monad is the centre. Note 21, page 123. In an address at Heidelberg, in 1889, Dr. Hertz said : — "I am here to support the assertion that light of every kind is itself an electrical phenomenon — the light of the sun, the light of a caudle, the light of a glow-worm. Take away from the world electricity, and light disappears." — Miscellaneous Papers, page 31.3.) Again (page 325), "Thus far, the experiments In carrying them out we are decidedly working in the region of optics. In planning the experiments, in describing them Explanatory Notes. 229 we no longer think electrically, but optically. We no longer see currents flowing in the conductors and electricities accumu- lating upon them : we only see the waves in the air, see how they intersect and die out and unite together, how they strengthen and weaken each other. Starting with purely electrical phenomena, we have gone on step by step until we find ourselves in the region of purely optical phenomena." Hertz failed to observe the conversion of potential into kinetic energy. So long as he contemplated polarised force between the particles of the conductor, or between the surfaces of two conductors, the phenomena were electrical. But when contact was established between the electrified particles, or the two electrified conductors, the potential energy was converted into kinetic energy, and from that stage in the operations the phenomena belonged to the sphere of optics. Note 22, page 124. Hertz thus describes the results of his experiments : — Let sparks from any induction-coil pass between knobs, and let the knobs be drawn so far apart that the sparks fail to pass ; if, now, the flame of a candle be brought near, the sparking begins again . . The flames of gas, wood, benzine, etc., all act in the same way. The non-luminous flames of alcohol and of the Bunsen burner exhibit the same effect .... From a small hydrogen flame scarcely any effect could be obtained. The light fi'om platinum glowing at a white heat in a flame, or through the action of an electric current, a powerful phosphorus flame burning quite near the spark, and burning sodium and potassium, all proved to be inactive. So also was burning sulphur ; but this can only have been on account of the feebleness of the flame, for the flame of burning carbon bisulphide produced some effect. Magnesium light produced a far more powerful effect than any of the above sources : its action extended to about the distance of a metre. 230 Molecular Forces and Newtonian Laws. The lime-light, produced by means of coal-gas and oxygen, was somewhat weaker, and acted up to a distance of half a metre: the action was mainly due to the jet itself : it made no great diflference whether the lime-cylinder was brought into the flame or not. On no occasion did I obtain a decisive effect from sun- light at any time of the day or year at which I was able to test it. When the sunlight was concentrated by means of a quartz lens upon the spark there was a slight action ; but this was obtained equally when a glass lens was used, and must, therefore, be attributed to the heating. But, of all sources of light the electric arc is by far the most effective ; it is the only one which can compete with the spark." — (^Electric Waves, pages 77-78.) Note 2.3, page 134. " From the presence of oxygen in the air, the latter is, as a whole, a magnetic medium of no small power." — (Faraday's Experimental Researches in Electricity, Art. 2791.) Note 24, page 143. "Diamagnetic bodies in media more diamagnetic than themselves, would have the polar conditions of paramagnetic bodies ; and, in like manner, paramagnetic conductors in media more paramagnetic than themselves, would have the polarity of diamagnetic bodies." — (Faraday's Experimental Researches in Electricity, Art. 2883.) Note 2-5, page 148. If the sun has anything to do with the magnetism of the globe, then it is probable that part of its effect is due to the action of the light that comes from it; and in that expectation the air seems most strikingly placed round our sphere, investing it with a transparent diamagnetic, which, therefore, is permeable by his rays, and at the same time moving with Explanatory Notes. 231 great velocity across them. Such conditions seem to suggest the possibility of magnetism being there generated." — (Faraday's Experimental Besearches in Electricity, Art. 2453.) In this passage Faraday anticipates the view given ia the text. He speaks, indeed, of the air as a diamagnetic, but elsewhere he speaks of it expressly as a paramagnetic of no small power. No magnetism is generated by the motion of a diamagnetic through heat rays, but it is generated by the motion of a paramagnetic. Note 26, page 167. In the following passage Faraday expresses the view that the annual and diurnal variations of the needle may be due to changes in the magnetic property of the atmosphere : — " It is hardly necessary for me to say here that this oxygen cannot exist in the atmosphere, exerting such a remarkable and high amount of magnetic force, without having a most important influence on the disposition of the magnetism of the earth as a planet, especially if it be remembered that its magnetic condition is greatly altered by variations in its density and by variations of temperature. I think I see here the real cause of many of the variations of that force, which have been, and are now, so carefully watched on different parts of the surface of the globe. The daily variations and the annual variations both seem likely to come under it ; also, very many of the irregular continual variations which the photographic process of record renders so beautifully manifest." — (Eayierimental Besearches in Electricity, Art. 2796.) Any increase or diminution of the magnetic property of the atmosphere might affect the magnetic intensity, but not the direction of the needle, which is due to the direction of the solar rays. Increased density, however, would alter the direction of the solar rays by increasing refraction. It is. interesting to observe the prevailing idea in Faraday's mind that terrestrial magnetism is to a great extent an atmospheric phenomena. 232 Molecular Forces and Newtonian Laws. Note 27, page 189. Referring to a series