Part 20

The great difference in the sensibility to different colours of the eyes of dark and fair persons when the light fell upon the _fovea centralis_, led Maxwell to the discovery of the extreme want of sensibility of this portion of the retina to blue light. This he made manifest by looking through a bottle containing solution of chrome alum, when the central portion of the field of view appears of a light red colour for the first second or two.

A more important discovery was that of double refraction temporarily produced in viscous liquids. Maxwell found that a quantity of Canada balsam, if stirred, acquired double-refracting powers, which it retained for a short period, until the stress temporarily induced had disappeared.

But Maxwell's investigations in optics must be regarded as his play; his real work lay in the domains of electricity and of molecular physics.

In 1738 Daniel Bernouilli published an explanation of atmospheric pressure on the hypothesis that air consists of a number of minute particles moving in all directions, and impinging on any surface exposed to their action. In 1847 Herapath explained the diffusion of gases on the hypothesis that they consisted of perfectly hard molecules impinging on one another and on surfaces exposed to them, and pointed out the relation between their motion and the temperature and pressure of a gas. The present condition of the molecular theory of gases, and of molecular science generally, is due almost entirely to the work of Joule, Clausius, Boltzmann, and Maxwell. To Maxwell is due the general method of solving all problems connected with vast numbers of individuals--a method which he called the statistical method, and which consists, in the first place, in separating the individuals into groups, each fulfilling a particular condition, but paying no attention to the history of any individual, which may pass from one group to another in any way and as often as it pleases without attracting attention. Maxwell was the first to estimate the average distance through which a particle of gas passes without coming into collision with another particle. He found that, in the case of hydrogen, at standard pressure and temperature, it is about 1/250000 of an inch; for air, about 1/389000 of an inch. These results he deduced from his experiments on viscosity, and he gave a complete explanation of the viscosity of gases, showing it to be due to the "diffusion of momentum" accompanying the diffusion of material particles between the passing streams of gas.

One portion of the theory of electricity had been considerably developed by Cavendish; the application of mathematics to the theory of attractions, and hence to that of electricity, had been carried to a great degree of perfection by Laplace, Lagrange, Poisson, Green, and others. Faraday, however, could not satisfy himself with a mathematical theory based upon direct action at a distance, and he filled space, as we have seen, with tubes of force passing from one body to another whenever there existed any electrical action between them. These conceptions of Faraday were regarded with suspicion by mathematicians. Sir William Thomson was the first to look upon them with favour; and in 1846 he showed that electro-static force might be treated mathematically in the same way as the flow of heat; so that there are, at any rate, two methods by which the fundamental formulæ of electro-statics can be deduced. But it is to Maxwell that mathematicians are indebted for a complete exposition of Faraday's views in their own language, and this was given in a paper wherein the phenomena of electro-statics were deduced as results of a stress in a medium which, as suggested by Newton and believed by Faraday, might well be that same medium which serves for the propagation of light; and "the lines of force" were shown to correspond to an actual condition of the medium when under electrical stress. Maxwell, in fact, showed, not only that Faraday's lines formed a consistent system which would bear the most stringent mathematical analysis, but were more than a conventional system, and might correspond to a state of stress actually existing in the medium through which they passed, and that a tension along these lines, accompanied by an equal pressure in every direction at right angles to them, would be consistent with the equilibrium of the medium, and explain, on mechanical principles, the observed phenomena. The greater part of this work he accomplished while an undergraduate at Cambridge. He showed, too, that Faraday's conceptions were equally applicable to the case of electro-magnetism, and that all the laws of the induction of currents might be concisely expressed in Faraday's language. Defining the positive direction through a circuit in which a current flows as the direction in which a right-handed screw would advance if rotating with the current, and the positive direction around a wire conveying a current as the direction in which a right-handed screw would rotate if advancing with the current, Maxwell pointed out that the lines of magnetic force due to an electric current always pass round it, or through its circuit, in the positive direction, and that, _whenever the number of lines of magnetic force passing through a closed circuit is changed, there is an electro-motive force round the circuit represented by the rate of diminution of the number of lines of force which pass through the circuit in the positive direction_.

The words in italics form a complete statement of the laws regulating the production of currents by the motion of magnets or of other currents, or by the variation of other currents in the neighbourhood. Maxwell showed, too, that Faraday's electro-tonic state, on the variation of which induced currents depend, corresponds completely with the number of lines of magnetic force passing through the circuit.

He also showed that, when a conductor conveying a current is free to move in a magnetic field, or magnets are free to move in the neighbourhood of such a conductor, _the system will assume that condition in which the greatest possible number of lines of magnetic force pass through the circuit in the positive direction_.

But Maxwell was not content with showing that Faraday's conceptions were consistent, and had their mathematical equivalents,--he proceeded to point out how a medium could be imagined so constituted as to be able to perform all the various duties which were thus thrown upon it. Assuming a medium to be made up of spherical, or nearly spherical, cells, and that, when magnetic force is transmitted, these cells are made to rotate about diameters coinciding in direction with the lines of force, the tension along those lines, and the pressure at right angles to them, are accounted for by the tendency of a rotating elastic sphere to contract along its polar axis and expand equatorially so as to form an oblate spheroid. By supposing minute spherical particles to exist between the rotating cells, the motion of one may be transmitted in the same direction to the next, and these particles may be supposed to constitute electricity, and roll as perfectly rough bodies on the cells in contact with them. Maxwell further imagined the rotating cells, and therefore, _à fortiori_, the electrical particles, to be extremely small compared with molecules of matter; and that, in conductors, the electrical particles could pass from molecule to molecule, though opposed by friction, but that in insulators no such transference was possible. The machinery was then complete. If the electric particles were made to flow in a conductor in one direction, passing between the cells, or _molecular vortices_, they compelled them to rotate, and the rotation was communicated from cell to cell in expanding circles by the electric particles, acting as idle wheels, between them. Thus rings of magnetic force were made to surround the current, and to continue as long as the current lasted. If an attempt were made to displace the electric particles in a dielectric, they would move only within the substance of each molecule, and not from molecule to molecule, and thus the cells would be deformed, though no continuous motion would result. The deformation of the cells would involve elastic stress in the medium. Again, if a stream of electric particles were started into motion, and if there were another stream of particles in the neighbourhood free to flow, though resisted by friction, these particles, instead of at once transmitting the rotary motion of the cells on one side of them to the cells on the other side, would at first, on account of the inertia of the cells, begin to move themselves with a motion of translation opposite to that of the primary current, and the motion would only gradually be destroyed by the frictional resistance and the molecular vortices on the other side made to revolve with their full velocity. A similar effect, but in the opposite direction, would take place if the primary current ceased, the vortices not stopping all at once if there were any possibility of their continuing in motion. The imaginary medium thus serves for the production of induced currents.

The mechanical forces between currents and magnets and between currents and currents, as well as between magnets and currents, were accounted for by the tension and pressure produced by the molecular vortices. When currents are flowing in the same direction in neighbouring conductors, the vortices in the space between them are urged in opposite directions by the two currents, and remain almost at rest; the lateral pressure exerted by those on the outside of the conductors is thus unbalanced, and the conductors are pushed together as though they attracted each other. When the currents flow in opposite directions in parallel conductors, they conspire to give a greater velocity to the vortices in the space between them, than to those outside them, and are thus pushed apart by the pressure due to the rotation of the vortices, as though they repelled each other. In a similar way, the actions of magnets on conductors conveying currents may be explained. The motion of a conductor across a series of lines of magnetic force may squeeze together and lengthen the threads of vortices in front, and thus increase their speed of rotation, while the vortices behind will move more slowly because allowed to contract axially and expand transversely. The velocity of the vortices thus being greater on one side of the wire than the other, a current must be induced in the wire. Thus the current induced by the motion of a conductor in a magnetic field may be accounted for.

This conception of a medium was given by Maxwell, not as a theory, but to show that it was possible to devise a _mechanism_ capable, in imagination at least, of producing all the phenomena of electricity and magnetism. "According to our theory, the particles which form the partitions between the cells constitute the matter of electricity. The motion of these particles constitutes an electric current; the tangential force with which the particles are pressed by the matter of the cells is electro-motive force; and the pressure of the particles on each other corresponds to the tension or potential of the electricity."

When a current is maintained in a wire, the molecular vortices in the surrounding space are kept in uniform motion; but if an attempt be made to stop the current, since this would necessitate the stoppage of the vortices, it is clear that it cannot take place suddenly, but the energy of the vortices must be in some way used up. For the same reason it is impossible for a current to be suddenly started by a finite force. Thus the phenomena of self-induction are accounted for by the supposed medium.

The magnetic permeability of a medium Maxwell identified with the density of the substance composing the rotating cells, and the specific inductive capacity he showed to be inversely proportional to its elasticity. He then proved that the ratio of the electro-magnetic unit to the electro-static unit must be equal to the velocity of transmission of a transverse vibration in the medium, and consequently proportional to the square root of the elasticity, and inversely proportional to the square root of the density. If the medium is the same as that engaged in the propagation of light, then this ratio ought to be equal to the velocity of light, and, moreover, in non-magnetic media, the refractive index should be proportional to the square root of the specific inductive capacity. The different measurements which had been made of the ratio of the electrical units gave a mean very nearly coinciding with the best determinations of the velocity of light, and thus the truth underlying Maxwell's speculation was strikingly confirmed, for the velocity of light was determined by purely electrical measurements. In the case also of bodies whose chemical structure was not very complicated, the refractive index was found to agree fairly well with the square root of the specific inductive capacity; but the phenomenon of "residual charge" rendered the accurate measurement of the latter quantity a matter of great difficulty. It therefore appeared highly probable that light is an electro-magnetic disturbance due to a motion of the electric particles in an insulating medium producing a strain in the medium, which becomes propagated from particle to particle to an indefinite distance. In the case of a conductor, the electric particles so displaced would pass from molecule to molecule against a frictional resistance, and thus dissipate the energy of the disturbance, so that true (_i.e._ metallic) conductors must be nearly impervious to light; and this also agrees with experience.

Maxwell thus furnished a complete theory of electrical and electro-magnetic action in which all the effects are due to actions propagated in a medium, and direct action at a distance is dispensed with, and exposed his theory successfully to most severe tests. In his great work on electricity and magnetism, he gives the mathematical theory of all the above actions, without, however, committing himself to any particular form of mechanism to represent the constitution of the medium. "This part of that book," Professor Tait says, "is one of the most splendid monuments ever raised by the genius of a single individual.... There seems to be no longer any possibility of doubt that Maxwell has taken the first grand step towards the discovery of the true nature of electrical phenomena. Had he done nothing but this, his fame would have been secured for all time. But, striking as it is, this forms only one small part of the contents of this marvellous work."

CONCLUSION.

SOME OF THE RESULTS OF FARADAY'S DISCOVERIES, AND THE PRINCIPLE OF ENERGY.

In early days, _the spirit of the amber_, when aroused by rubbing, came forth and took to itself such light objects as it could easily lift. Later on, and the spirit gave place to the _electric effluvium_, which proceeded from the excited, or charged, body into the surrounding space. Still later, and a fluid, or two fluids, acting directly upon itself, or upon matter, or on one another, through intervening space without the aid of intermediate mechanism, took the place of the electric effluvium--a step which in itself was, perhaps, hardly an advance. Then came the time for accurate measurement. The simple _observation_ of phenomena and of the results of experiment must be the first step in science, and its importance cannot be over-estimated; but before any quantity can be said to be known, we must have learned how to _measure_ it and to reproduce it in definite amounts. The great law of electrical action, the same as that of gravitation--the law of the inverse square--soon followed, as well as the associated fact that the electrification of a conductor resides wholly on its surface, and there only in a layer whose thickness is too small to be discovered. The fundamental laws of electricity having thus been established, there was no limit to the application of mathematical methods to the problems of the science, and, in the hands of the French mathematicians, the theory made rapid advances. George Green, of Sneinton, Nottingham, introduced the term "potential" in an essay published by subscription, in Nottingham, in 1828, and to him we are indebted for some of our most powerful analytical methods of dealing with the subject; but his work remained unappreciated and almost unknown until many of his theorems had been rediscovered. But the idea of a body acting where it is not, and without any conceivable mechanism to connect it with that upon which it operates, is repulsive to the minds of most; and, however well such a theory may lend itself to mathematical treatment and its consequences be borne out by experiment, we still feel that we have not solved the problem until we have traced out the hidden mechanism. The pull of the bell-rope is followed by the tinkling of the distant bell, but the young philosopher is not satisfied with such knowledge, but must learn "what is the particular go of that." This universal desire found its exponent in Faraday, whose imagination beheld "lines" or "tubes of force" connecting every body with every other body on which it acted. To his mind these lines or tubes had just as real an existence as the bell-wire, and were far better adapted to their special purposes. Maxwell, as we have seen, not only showed that Faraday's system admitted of the same rigorous mathematical treatment as the older theory, and stood the test as well, but he gave reality to Faraday's views by picturing a mechanism capable of doing all that Faraday required of it, and of transmitting light as well. Thus the problem of electric, magnetic, and electro-magnetic actions was reduced to that of strains and stresses in a medium the constitution of which was pictured to the imagination. Were this theory verified, we might say that we know at least as much about these actions as we know about the transmission of pressure or tension through a solid.

With regard to the _nature_ of electricity, it must be admitted that our knowledge is chiefly negative; but, before deploring this, it is worth while to inquire what we mean by saying that we know what a thing is. A definition describes a thing in terms of other things simpler, or more familiar to us, than itself. If, for instance, we say that heat is a form of energy, we know at once its relationship to matter and to motion, and are content; we have described the constitution of heat in terms of simpler things, which are more familiar to us, and of which we _think_ we know the nature. But if we ask what _matter_ is, we are unable to define it in terms of anything simpler than itself, and can only trust to daily experience to teach us more and more of its properties; unless, indeed, we accept the theory of the vortex atoms of Thomson and Helmholtz. This theory, which has recently been considerably extended by Professor J. J. Thomson, the present occupier of Clerk Maxwell's chair in the University of Cambridge, supposes the existence of a perfect fluid, filling all space, in which minute whirlpools, or vortices, which in a perfect fluid can be created or destroyed only by superhuman agency, form material atoms. These are _atoms_, that is to say, they defy any attempts to sever them, not because they are infinitely hard, but because they have an infinite capacity for _wriggling_, and thus avoid direct contact with any other atoms that come in their way. Perhaps a theory of electricity consistent with this theory of matter may be developed in the future; but, setting aside these theories, we may possibly say that we know as much about electricity as we know about matter; for while we are conversant with many of the properties of each, we _know_ nothing of the ultimate nature of either.