The Examiners give notice, that the following is the subject for the prize to be adjudged in 1857:—

In his essay, to which the prize was adjudged, and which occupies sixty-eight pages of quarto, Maxwell considered in the first place the hypothesis of Laplace, and showed that to secure stability the irregularity of the ring must be enormously great. Speaking of Laplace’s conclusion that the rings must be irregular, Maxwell says:—

The following extract shows how Maxwell mentally realised every problem which he considered:—

The investigation of the stability of the motion of a solid ring, otherwise uniform but loaded with a heavy particle upon its circumference, led to the conclusion that the mass of the particle must be about four and a half times that of the rest of the ring—

The investigation of the motion of a ring composed of a continuous liquid, led to the result that the waves set up in the ring would cause it to break up into a number of drops which might revolve as satellites about Saturn; but if the condition of stability was not fulfilled, they would coalesce, forming a smaller number of larger drops, until the condition of stability was secured; and the same would be the case if the ring were supposed to consist of a number of concentric narrow rings. The liquid ring, therefore, did not afford a more satisfactory result than the solid one, though it appeared that the internal friction would produce no sensible effect, and Maxwell had recourse to “the dusky-ring, which is something like the state of the air supposing the siege of Sebastopol conducted from a forest of guns 100 miles one way and 30,000 miles the other, and the shot never to stop but go spinning away round a circle radius 170,000 miles.”[254] This, however, is not the order in which the investigations appear in the paper before us.

Having dismissed the assumption of the solid rings, Maxwell investigated the effect of disturbance on a ring of small transverse section, the parts of which are not rigidly connected. The disturbances he treated as made up of “harmonic” elements, according to Fourier’s method; and, first treating the ring as a number of equal satellites revolving round the planet, he found that such a ring “can always be rendered stable by increasing the mass of the central body and the angular velocity of the ring.” If the ring consist of 100 satellites, the mass of the planet must exceed 4352 times that of the ring in order to secure stability for all displacements. “If this condition be not fulfilled,... then, although the motion depending upon long undulations may remain stable, the short undulations will increase in amplitude till some of the neighbouring satellites are brought into collision.” The satellites of such a ring, when the condition of stability is fulfilled, admit of four vibrations in different periods in ellipses about their mean positions, and these vibrations will be transmitted as waves with different velocities round the ring, so that the form of the ring at any instant resembles “that of a string of beads forming a re-entering curve, nearly circular, but with a small variation of distance from the centre,” forming a number of “regular curves of transverse displacement at regular intervals round the circle. Besides these, there are waves of condensation and rarefaction, the effect of longitudinal displacement.” Any external disturbance, such as a satellite or wave in another ring, will produce a forced wave in the ring, and if the angular velocity of the external disturbing cause around the ring coincide, or nearly coincide, with the velocity of one of the free waves of the ring, the amplitude of the forced wave will increase indefinitely until the ring is destroyed; but if this condition is not fulfilled, the forced wave will accompany the disturbing cause around the ring as the tide follows the moon.

The effect of one ring upon another is to produce in it a series of forced waves travelling with the same angular velocity as the free waves in the disturbing ring. Hence in a system of two rings “there will be eight waves in each ring, and the corresponding waves in the two rings will act and react on each other, so that, strictly speaking, every one of the waves will be in some measure a forced wave, although the system of eight waves will be the free motion of the two rings taken together.”

The dynamical stability of a ring of satellites is explained by the consideration that when one of the satellites, in consequence of its oscillations, moves with more than its mean velocity, and thus gets in front of its proper position, it will be carried farther away from the planet, and thus not only will its linear velocity be diminished, but, in virtue of its increased distance, its angular velocity will be still farther diminished and, lagging behind, it will fall back into its proper position and, oscillating through it with a velocity less than its mean, will approach the planet and the reverse action will take place.

After considering the manner in which the ring will break up if the condition of stability is not fulfilled, Maxwell takes up the question of “the dusky ring,” consisting of innumerable small particles resembling “a shower of rain, hail, or cinders.” For the stability of such a ring its average density must not exceed StartFraction 1 Over 300 EndFraction of that of the planet, and the density of Saturn being only ·7505, it follows that the average density of the ring cannot greatly exceed that of air at ordinary pressure. Laplace showed that for a ring to rotate as a whole with uniform velocity about Saturn, the density of the planet cannot exceed 1·3 times that of the ring. Hence the particles must move independently, or in a series of concentric rings.

In the case of concentric rings of satellites, their mutual disturbances will destroy one another if the velocity of any one of the four free waves of one coincide, or nearly coincide, with that of any free wave in another; and it is impossible that there should be any great number of rings without this condition frequently recurring.

The transparency of the inner ring, which allows the planet to be seen through it without distortion, and the observed changes in the configuration of the rings themselves, all favour this conclusion.

The apparatus constructed by Maxwell to illustrate the motions of the satellites in the rings has been already referred to.[255] It is an arrangement in which ivory balls are made to go through the motions belonging to the first or fourth of the four series of waves above mentioned, except that the balls describe circles instead of ellipses about their mean positions. We give the description as printed in the essay; the apparatus itself is in the Cavendish Laboratory.

The instrument stands on a pillar A (Figs. 7 and 8), in the upper part of which turns the cranked axle CC. On the parallel parts of this axle are placed two wheels, RR and TT, each of which has thirty-six holes, at equal distance, in a circle near its circumference. The two circles are connected by thirty-six small cranks of the form KK, the extremities of which turn in the corresponding holes of the two wheels. The axle of the crank K which passes through the hole in the wheel S is bored so as to hold the end of the bent wire which carries the satellite S. This wire may be turned in the hole so as to place the bent part carrying the satellite at any angle with the crank. A pin P, which passes through the top of the pillar, serves to prevent the cranked axle from turning; and a pin Q, passing through the pillar horizontally, may be made to fix the wheel R by inserting it in a hole in one of the spokes of that wheel. There is also a handle H, which is in one piece with the wheel T, and serves to turn the axle.

Now suppose the pin P taken out, so as to allow the cranked axle to turn, and the pin Q inserted in its hole so as to prevent the wheel R from revolving; then if the crank C be turned by means of the handle H, the wheel T will have its centre carried round in a vertical circle, but will remain parallel to itself during the whole motion, so that every point in its plane will describe an equal circle, and all the cranks K will be made to revolve exactly as the large crank C does. Each satellite will therefore revolve in a small circular orbit in the same time with the handle H, but the position of each satellite in that orbit may be arranged as we please, according as we turn the wire which supports it in the end of the crank.

In Fig. 8, which gives a front view of the instrument, the satellites are so placed that each is turned 60 Superscript ring farther round in its socket than the one behind it. As there are thirty-six satellites, this process will bring us back to our starting-point after six revolutions of the direction of the arm of the satellite; and therefore, as we have gone round the ring once in the same direction, the arm of the satellite will have overtaken the radius of the ring five times.

Hence there will be five places where the satellites are beyond their mean distance from the centre of the ring, and five where they are within it, so that we have here a series of five undulations round the circumference of the ring. In this case the satellites are crowded together when nearest to the centre....

Now suppose the cranked axle C to be turned, and all the small cranks K to turn with it, as before explained, every satellite will then be carried round on its arm and in the same direction; but, since the direction of the arms of different satellites is different, their phases of revolution will preserve the same difference, and the system of satellites will still be arranged in five undulations, only the undulations will be propagated round the ring in the direction opposite to that of the revolution of the satellites.

If the satellites are arranged as in Fig. 8, where each is more advanced in phase as we go round the ring, the wave will travel in the direction opposite to that of rotation, but if they are arranged as in Fig. 9, where each satellite is less advanced in phase as we go round the ring, the wave will travel in the direction of rotation.

We may now show these motions of the satellites among each other, combined with the motion of rotation of the whole ring. For this purpose we put in the pin P, so as to prevent the crank axle from turning, and take out the pin Q, so as to allow the wheel R to turn. If we then turn the wheel T, all the small cranks will remain parallel to the first crank, and the wheel R will revolve at the same rate as T. The arm of each satellite will continue parallel to itself during the motion, so that the satellite will describe a circle whose centre is at a distance from the centre of R, equal to the arm of the satellite, and measured in the same direction. In our theory of real satellites each moves in an ellipse, having the central body in its focus, but this motion in an eccentric circle is sufficiently near for illustration. The motion of the waves relative to the ring is the same as before. The waves of the first kind (Fig. 8) travel faster than the ring itself, and overtake the satellites, those of the fourth kind (Fig. 9) travel slower and are overtaken by them.

This paper was characterised by the late Astronomer Royal as “one of the most remarkable applications of Mathematics to Physics that I have ever seen.”

6. But notwithstanding the investigations above referred to, and many other original papers on almost every branch of Physical Science, it is for his researches in Electricity and in Molecular Science that Maxwell stands pre-eminent among the men of science of the present century. After taking his degree in 1854, Maxwell read through Faraday’s Experimental researches, a course which he always recommended his students to follow. In Faraday he found a mind essentially of his own type. Thoroughly conversant himself with the Theory of Attractions as developed in Mathematical Treatises, and with the laws of electrical action as illustrated by Sir William Thomson in his paper “on the Uniform motion of heat in homogeneous solid bodies, and its connection with the Mathematical Theory of Electricity,” a paper published in the Cambridge Mathematical Journal, February 1842, and “on a Mechanical representation of Electric, Magnetic, and Galvanic Forces,” published in the Cambridge and Dublin Mathematical Journal, January 1847, Maxwell saw the connection between Faraday’s point of view and the method of research adopted by the Mathematicians. He used to say that he had not a good nose to smell heresy, but whatever was good and true Maxwell would detect beneath the mass of misconception, or even falsehood, which had gathered round it, and which caused its rejection by nearly every one else without inquiry. Faraday’s conception of a medium he adopted as a guide throughout his electrical researches.

Until the sixteenth century all that was known respecting electricity was the one fact that amber when rubbed possesses the power of attracting light bodies. This property was shown (Physiologia Nova, 1600) to be possessed by a variety of substances by Dr. Gilbert of Colchester, who was Physician to Queen Elizabeth, and who may be regarded as the founder of the Science of Electricity. From this time rapid strides were made in the experimental portion of the science, and the law according to which the attraction or repulsion between two small bodies charged with electricity varies with the charges, and the distance between them, was determined by Coulomb with his torsion balance, an instrument whose value to the experimental investigator can hardly be over-estimated. But it is to Cavendish (1771-1781) that we are mainly indebted for the foundation of the Mathematical Theory of Electricity, and for the highest experimental evidence of the law of electrical action. As the preparation for the press of The Electrical Researches of the Honourable Henry Cavendish was the last of Maxwell’s contributions to science, the work being published only a few weeks before his death, we shall again have to refer to Cavendish’s investigations, and need only state that his experiments proved conclusively, and in the best possible manner as far as the instruments at his disposal would allow, that the attraction or repulsion between two small charged bodies varies directly as the product of their charges, and inversely as the square of the distance between them, so that the law of electrical action is the same as Newton’s law of gravitation, except that the stress between similarly charged bodies is repulsive, and that between dissimilarly charged bodies attractive. After Cavendish’s time comparatively little was added to the theory of statical electricity, if we except the elaborate mathematical investigations of particular problems by Poisson, and the papers of George Green, which until recently were read by few, and appreciated by only two or three, until Faraday took up the subject. Most of Cavendish’s work remained unpublished and unknown, and some of his results were independently obtained by Faraday. It is difficult to conceive what would have been the effect on Faraday’s mind of perusing Cavendish’s “thoughts on electricity,” as well as his own accounts of his experiments. Perhaps it is best for the world that Faraday was left to work and think on independent lines; certainly it has been a boon to Mathematicians and Physicists alike that Maxwell has appeared to expound and develop, if not to perfect, the work of both.

The mathematical theory of attractions had, prior to the time of Faraday, attained a very high degree of development in the hands of Laplace, Lagrange, Poisson, and others, and could be applied to the solution of many very interesting problems in electricity. But Faraday was not satisfied with the hypothesis of direct action at a distance between charges of electricity, and held that there must be some mechanism by which electric and electromagnetic actions can be communicated from point to point. Not all the arguments by which he supported this view are conclusive, for the force upon an electrified body and the induced electrification of any conductor will be the same whether we adopt the hypothesis of direct action at a distance or of the transmission of electrical action in lines, straight or curved, through an intervening medium. But any view, whether the arguments in its favour are conclusive or not, is of value if it lead us to inquire more closely into the mechanism by which a phenomenon is brought about; and thus Faraday’s conception of lines of force, transmitted through a medium, and exerting tension and pressure wherever they are to be found, are of more value as an instrument of mental research than Weber’s Theory of Electro-magnetism, however perfect the latter may be from a mathematical point of view.

The following quotation, from the preface to the Electricity and Magnetism, gives Maxwell’s views of Faraday in his own words:—[256]

Suppose a small positively electrified body to start from a point close to a positively electrified surface, and suppose it to move always in the direction in which it is urged by the force acting on it, it will, of course, be repelled by the surface, and will move away along some path straight or curved, and will continue to move indefinitely, the force diminishing as it proceeds, unless it meet with a negatively electrified surface, which will attract it, and coming into contact with this surface its career will terminate. The path traced out by such a small electrified body constitutes Faraday’s line of force, which is therefore a line whose direction at any point is that of the resultant force at that point. Such lines of force always proceed from positively electrified surfaces, and terminate upon negatively electrified surfaces; or, failing this, they must proceed to infinity. Lines of force proceeding from a positively electrified body placed in a room, unless there be other negatively charged bodies in the neighbourhood, will in general terminate upon the walls, floor, and ceiling of the room, or upon objects in the room in electrical communication with these. Faraday thus conceived the whole of the space in which electrical force acts to be traversed by lines of force which indicate at every point the direction of the resultant force at that point. But Faraday went further than this: he conceived the notion of causing the lines of force to represent also the intensity of the force at every point, so that when the force is great the lines might be close together, and far apart when the force is small; and since the force in the neighbourhood of a small charged body is proportional to the charge, he endeavoured to accomplish this object by drawing from every positively electrified surface a number of lines of force proportional to its charge, and causing a similar number of lines of force to terminate in every negatively electrified surface. In a paper entitled “On Faraday’s Lines of Force,” read before the Cambridge Philosophical Society on December 10th, 1855, and February 11th, 1856, Maxwell showed that if a system of lines could be drawn according to Faraday’s method, then, in virtue of the law of electrical action being that of the inverse square of the distance, the number of lines of force passing through a unit area of any surface, drawn perpendicular to the direction of the force, is proportional to the magnitude of the force in the neighbourhood, and that the number of lines passing through the unit area of any other surface is proportional to the component of the force at right angles to that surface. Maxwell therefore imagined the positively electrified surfaces from which the lines started to be divided into areas, each containing one unit of electricity, and lines of force to be drawn through every point in each bounding line. These lines therefore divide the whole of space into “unit tubes,” whose boundaries are lines of force, and Maxwell showed that, in virtue of “the law of inverse squares,” the force at any point in any direction is inversely proportional to the area of the section of the unit tube of force made by a plane perpendicular to that direction. Maxwell further showed that on the negatively electrified surface upon which these tubes terminate, each tube will enclose one unit of negative electricity, and consequently, if a metallic surface be introduced so as to cut the lines of force, the surface being placed at right angles to the tube, a unit of negative electricity will be induced on each portion of the surface contained within the trace of a tube of force; and hence, in any isotropic medium, these unit tubes of force are also unit tubes of induction. If, therefore, a system of tubes of force be drawn in connection with any electrified system, and in accordance with this plan, the whole of the space in which the force acts will be divided into tubes each originating from a unit of positive electricity and terminating upon a unit of negative electricity, while the direction of the force at any point will be indicated by that of the tube, and the magnitude of the force will be inversely proportional to the area of the cross section of the tube. How, if the law of force had been any other than that of the inverse square, and tubes had been drawn starting from an electrified surface as above, and such that the area of any section of a tube is inversely proportional to the force across the section, these tubes would either leave spaces between them as they recede from the surface, or would intersect one another; so that it is only for the law of inverse squares that the system of tubes above described is possible. Faraday pointed out that there is not only a tension exerted along each line of force, but that the several lines exert a repulsion upon one another, and Maxwell showed that a tension along the lines of force, accompanied by an equal pressure in every direction at right angles to these lines, is consistent with the equilibrium of the medium. Taking an illustration from the flow of water in a river. Maxwell pointed out that the stream lines or paths along which particles of water flow, are analogous to lines of electric force, the velocity of the water being analogous to the intensity of the force. If the river be supposed to be divided into tubes, the boundaries of which are lines of flow, and if these tubes be so drawn that unit volume of water passes across a particular section of each tube in a second, then, if the flow be steady, unit volume of water will flow across every section of each tube in a second, since no water enters or leaves the tube except at its ends. Such tubes may be called unit tubes of flow, and if no tributaries enter the river there will be the same number of unit tubes crossing each section of the river. Where the bed widens the section of each tube increases, being always inversely proportional to the velocity of the water, and hence the number of unit tubes of flow which cut any unit of area in a cross section of the river will be proportional to the velocity of the water in the neighbourhood. Such a system of tubes, therefore, will represent both the direction of motion and velocity of the water at every point, and will exactly correspond, mutatis mutandis, with a system of unit tubes of electric force.

The following letter was addressed to Maxwell by Faraday on receiving a copy of the paper on “Lines of Force:”—

The paper, read before the Cambridge Philosophical Society, and published in vol. X. of their Proceedings, is confessedly only a translation of Faraday’s ideas into mathematical language, with illustrations and extensions, and it makes no attempt at explaining the nature of the action in the dielectric, or the mechanism by which the observed effects are brought about. About five years later, in a series of three papers communicated to the Philosophical Magazine in 1861 and 1862, Professor Maxwell gave a simple sketch of a system of mechanism, capable of producing not only the electrostatic effects above alluded to, but also of accounting for magnetic attraction, the action of electric currents upon one another, and upon magnets, and electromagnetic induction; but before giving an account of these papers it will be necessary briefly to mention the principal phenomena, an explanation of which was required.

The ordinary phenomena of magnetism, including the attraction between dissimilar and the repulsion between similar poles, as well as the still more familiar phenomena of the attraction of soft iron by a magnetic pole, are too well known to require more than a passing mention. Coulomb showed that the law of inverse squares obtained equally for magnetic repulsions as for electrical, so that the stress between two magnetic poles is proportional to the product of the strengths of the poles and inversely proportional to the square of the distance between them, provided the steel of which the magnets are composed is sufficiently hard to prevent the actions of the magnets on each other altering the strengths of their poles.

If a sheet of paper he supported horizontally above the poles of a magnet, and iron filings be sprinkled over the paper, each filing becomes magnetised by induction in the direction of the resultant magnetic force at the point where it is situated, and if the paper be gently tapped so as to overcome friction, the mutual attraction of the unlike poles in the filings causes them to adhere together in threads or filaments, the North pole of one filing attaching itself to the South pole of a neighbouring filing, and so on, the points of attachment all lying along a line of force. In this way the filings form a graphic representation of the lines of magnetic force, and it was this experiment which first suggested to Faraday the idea of the physical existence of such lines; and as he found it difficult to conceive of curved lines of force being due to “direct action at a distance” (Exp. Res. 1166), he considered that there must be some medium which is the vehicle both of magnetic and electric forces, and that such forces are propagated from particle to particle of the medium. Faraday also supposed that the same medium might serve as the vehicle for the transmission of light. The investigation of the properties of the medium necessary to account for observed electric and magnetic actions, the explanation of these actions, and the determination of the velocity of light from purely electro-magnetic considerations on the hypothesis of the existence of a such a medium constitute Maxwell’s greatest contribution to electrical science.

The action of an electric current upon a magnet was first observed by Œrsted. It is said that he made many attempts in his laboratory to discover an action between a magnet and a wire conveying a current, but in all his attempts he carefully placed the wire at right angles to the magnetic needle, and could detect no effect whatever. On attempting to repeat the experiment in the presence of his class he placed the wire parallel to the needle, and the latter immediately swung round and ultimately came to rest nearly at right angles to the wire. Whenever the North pole (i.e. the North seeking pole) of a magnet is brought near to a wire conveying a current, the pole tends to go round the wire in a certain direction, while the South (or South seeking) pole of the magnet tends to go round the wire in the opposite direction, and hence if the magnet be free to turn about its centre, the magnet will come to rest at right angles to the wire. Many memoriœ technicœ have been given for determining the manner in which a magnet will behave in the neighbourhood of a current. Maxwell’s rule was as follows:—Suppose a right-handed screw to be advancing in the direction of the current, and of necessity rotating as it advances, as if it were piercing a solid. The North pole of a magnet will always tend to move round the wire conveying the current in the direction in which such a screw rotates, while the South pole will tend to move in the opposite direction.

We may thus suppose every wire conveying a current to be surrounded by lines of magnetic force which form closed curves around the wire, and the direction of the force is that in which a right-handed screw would rotate if advancing with the current. In the case of a straight wire of infinite length, these curves are of course circles. Since action and reaction are equal and opposite, it follows that whatever be the mechanical force exerted by a current upon a pole of a magnet, the latter will always exert an equal and opposite force upon the wire or other conductor conveying the current. Many experiments have been devised to show this. Maxwell used to illustrate it in a very simple way. Having attached a piece of insulated copper wire to a small round plate of copper, he placed the plate at the bottom of a small beaker. A disc of sheet zinc was then cut of such size as to fit loosely in the beaker, a small “tail” of zinc being left attached to it; this was bent up and united to the copper wire above the top of the beaker, while the plate of zinc was suspended in a horizontal position an inch or two above the copper plate. The beaker was filled up with dilute sulphuric acid and placed on one pole of an electromagnet, some sawdust or powdered resin being placed in the liquid to show its movements. On exciting the magnet the liquid rotated in one direction, and on reversing the polarity of the magnet the direction of rotation was reversed. If the plates be suspended by a string, so that they can readily turn round in the beaker about a vertical axis, the action of the magnet on the current in the vertical wire will cause the plates to turn always in the direction opposite to that of the liquid.

The laws of the mechanical action of conductors conveying currents upon magnets and upon each other were investigated by Ampère in a series of experiments which were at once conclusive and exhaustive. These experiments were alluded to in the highest terms by Professor Maxwell. Any account of them would be out of place here, and we only refer to them as furnishing the experimental evidence for the statements which follow.

We have already described the manner in which magnetic lines of force may be supposed to surround a wire conveying a current. Now let such a wire be bent into a closed curve or ring-which need not necessarily be circular. The lines of force, which themselves form closed curves around the wire, will all pass in the same direction through the ring formed by the wire conveying the current, as if they were strung upon the wire, and hence the North pole of a magnet will tend to pass through the ring in the direction of the lines of force; and a moment’s reflection will show that this direction is that in which a right-handed screw would advance if rotating in the direction of the current in the wire. Hence, if the North pole of a magnet be brought near to such a small closed circuit, on the one side it will be attracted and tend to pass through the circuit; on the other side it will be repelled. The South pole of a magnet will be acted upon in precisely the opposite manner. Hence if a small magnetic needle be suspended within a coil of wire conveying a current, it will tend to set itself at right angles to the plane of the coil. Such an arrangement constitutes a galvanometer.

Now suppose that we have a small disc of steel of the same size and shape as the ring formed by the wire, and that this disc is magnetised so that one side is a north pole and the other a south pole. Such a disc will act upon external magnets in the same manner as the current if it he magnetised, so that a right-handed screw rotating with the current would enter at the south face and emerge at the north face. Such a magnetised disc is called a magnetic shell, and it will of course he acted upon by a magnet with forces exactly equal and opposite to those with which the magnet is acted upon by it. The magnetic lines of force proceeding from a circuit conveying an electric current are therefore the same as would proceed from the magnetic shell above described, the strength of the magnetisation being properly adjusted; in other words, the magnetic field around such a circuit is the same as that surrounding the magnetic shell, and hence it follows that two circuits, each conveying electric currents, will act upon one another in the same way as two magnetic shells whose circumferences coincide with the wires, and which are magnetised as above described.

Now if the shells be parallel and magnetised in the same direction, they will have their opposite faces presented towards each other, and will attract one another. If they are magnetised in the opposite directions they will repel one another. Similarly, two parallel circuits will attract one another if the currents be passing in the same direction in both, and will repel one another if they be going in opposite directions. Also two parallel wires, which may be considered as parts of such circuits, will attract one another when the currents in them are going in the same direction, and repel one another if they are going in the opposite directions. Maxwell’s rule for determining the manner in which a circuit conveying a current will behave in the presence of other currents or of magnets is a very simple expression of Faraday’s results. Defining the positive direction through a circuit as that in which a right-handed screw would advance if rotating with the current, he enunciated the rule thus:—

If a wire conveying a current be free to move in a magnetic field it will tend to set itself so that the greatest possible number of lines of magnetic force may pass through the circuit in the positive direction.

Since the magnetic field may be produced either by magnets or by electric currents themselves, as above described, this rule combined with the principle that action and reaction are equal and opposite will serve to determine the character of the action either upon circuits conveying currents or upon magnets in every possible case which may arise, and, in fact, embodies the magnificent results of Ampère’s investigations in this subject.

Previously to the experiments of Faraday the induction of electric currents was unknown. The principal phenomenon depending upon this action, which had been observed, and of which no satisfactory explanation had been offered, was that of Arago’s rotating disc. In this experiment a disc of copper was made to rotate rapidly in its own horizontal plane above a compass needle, when the needle was observed to follow the disc and rotate on its vertical pin. This experiment was subsequently repeated by Sir John Herschel and Mr. Babbage, who employed discs of various substances, and found that it was only when the discs were good conductors of electricity that Arago’s result was obtained. Faraday, in the first series of his Experimental Researches, describes an experiment in which a copper disc was made to rotate between the poles of an electro-magnet, while one electrode of a galvanometer was connected with the axis of the disc, and the other with a wire which was held in contact with the edge of the disc, which edge was amalgamated to secure a good connection. On spinning the disc a current was immediately obtained, the direction of which was reversed with that of the rotation. This experiment may be regarded as the starting-point of the dynamo machines of Wilde, Gramme, Siemens, and others, which seem destined to play so important a part in the civilised life of the future.

Faraday also showed that when two circuits are placed near to one another, if a current be started in one circuit there is an instantaneous current produced in the opposite direction in the neighbouring circuit, while on stopping the “primary” current a transient current in the same direction as the primary occurs in the other or “secondary” circuit. This experiment was the origin of the now well-known induction coil. Again, when the current was flowing steadily in the primary circuit, if the secondary circuit were brought nearer to it, a current was induced in the secondary in the direction opposite to that in the primary, and continued during the approach of the circuits. On removing the secondary circuit a transient current was set up in the same direction as that in the primary.

We cannot here spare space to trace the development of the laws of induced currents. The character of the action may in all cases be inferred from the very concise statement of Lenz, generally quoted as Lenz’s law, and which may be thus expressed:—

If a conductor move in a magnetic field, an electromotive force will be induced in the conductor which will tend to produce a current in such direction that the mechanical force upon the conductor tends to oppose its motion.

This law, taken in conjunction with the statements made above respecting the mechanical action in a magnetic field upon a conductor conveying a current, serves to determine the character of the induced current whenever a conductor moves in the neighbourhood of magnets or electric currents. Moreover, the starting of a current in a neighbouring circuit must have the same effect upon the wire as if the conductor were suddenly brought from an infinite distance into the position which it actually occupies. Hence Lenz’s law will apply to every case of induced currents.

Maxwell’s statement expresses the laws of induced currents quantitatively as well as qualitatively. It is as follows:—

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.

If, then, the number of magnetic lines of force passing through a circuit is diminished, there will be an electro-motive force round the circuit in the direction in which a right-handed screw would rotate if advancing along the lines of force; a line of force being always supposed to be drawn in the direction in which a north magnetic pole tends to move along it. If the number of lines of force passing through the circuit is increased, the electro-motive force will be in the opposite direction. This law can be deduced from that which expresses the mechanical action upon a circuit conveying a current when placed in a magnetic field together with the principle of the conservation of energy. That it may be numerically true all the quantities involved must be expressed in terms of the electromagnetic system of units.

The telephone is a beautiful example of the application of this law. Every movement of the iron disc in front of the pole of the magnet alters the number of magnetic lines of force passing through the coils of wire surrounding the pole; and hence induces a current in one direction or the other in the coil, which current, increasing or diminishing the strength of the magnetism in the receiving telephone, causes a corresponding motion in the iron disc of the receiver, which therefore emits sounds similar to those incident upon the receiving instrument.

From what has been stated it will appear that the motion of a conductor will produce a current therein only when the conductor is moving in a magnetic field, that is, a portion of space through which magnetic lines of force pass. Faraday supposed that a conductor under these circumstances was thrown into a peculiar condition, which he termed “the electrotonic state,” and that a current was induced whenever this state varied. Maxwell showed that this electrotonic state, on the variations of which the induced current in a circuit depends, corresponds to the number of magnetic lines of force which pass through the circuit. Because every change in this quantity involved the action of electromotive force, its relations to electromotive force being the same as those of momentum to force in dynamics, he called the quantity itself electromagnetic momentum. Maxwell’s conception of the physical nature of this quantity will be described presently.

The determination of the laws of self-induction in electric currents is another of Faraday’s many contributions to electrical science. After one of the Friday evening lectures at the Royal Institution, a certain Mr. Jenkin informed Faraday that when he broke the connection of the circuit in his electromagnet by separating two pieces of wire which he held in his hands, he felt a smart shock. Faraday said that this was the only suggestion, out of a very great number, made to him by ordinary members of a popular audience which ever led to any result. On investigating the matter, Faraday found that when a current is flowing in a coil of wire if the battery be removed there is a tendency for the current to continue after the removal of the battery, and that this tendency is increased by increasing the number of turns of wire in the coil, and still more so by inserting soft iron in the centre of the coil. This tendency does not depend so much on the length of the wire as upon the relative positions of its parts, and if the wire be first doubled and then wound into a coil the tendency disappears. If a few Grove’s cells send a current through a short straight piece of wire and the circuit be broken a very feeble spark will be seen on breaking, but if a large electromagnet be introduced into the circuit a very much brighter spark will appear on breaking contact, though the current sent by the battery is feebler. Thus, when a current flows in such a coil its behaviour reminds us of that of water flowing in a pipe which, when an obstruction is suddenly introduced so as to stop the flow, exerts an enormous pressure for a short time upon the pipe and obstruction, in virtue of the momentum which the water has acquired; but that the action is not due to any momentum actually possessed by the moving electricity is shown by the fact that it depends on the configuration of the wire. This property of a coil is called self-induction. If the poles of an electro-magnet be joined by a wire of great resistance as well as by the battery, when the battery is removed a considerable current will flow through the wire. This current Faraday called the extra-current. It is more generally referred to as the self-induction current.

A similar action takes place when connection is made between a battery and a coil. The current does not at once acquire its full value, but for a short time goes on steadily increasing; the self-induction of the coil causing it to behave as if the current in it possessed considerable mass, which has in the first instance to be put into motion. All these actions are immediate consequences of the law of induced currents stated on p. 526.

There is a well-known experiment of Faraday in which a specimen of his heavy glass, or borate of lead, was placed between the poles of a powerful electro-magnet and a beam of plane polarised light was passed through the glass in the direction of the magnetic force. Faraday found that when the light passed from the north to the south pole of the magnet the plane of polarisation was turned through an angle in the same direction as a right-handed screw would rotate if piercing a solid and advancing with the light. When the light passed in the opposite direction, the rotation of the plane of polarisation was in the same direction with respect to the magnet, and therefore reversed with respect to the path of the light. In this respect the heavy glass under the influence of the magnet behaved differently from a solution of sugar which always turns the plane of polarisation of the light in the same direction with reference to its direction of transmission. This was the first experiment which showed any relation between light and magnetism, and indicated that the medium which serves as the vehicle of light—the luminiferous ether—must at least be affected by the presence of magnetic force, though the fact that the presence of ponderable matter is necessary to the production of this rotation, and that the direction of the rotation depends on the nature of the matter, renders it doubtful how far magnetic force affects the ether directly.

All transparent solids and liquids exhibit the same action on light in different degrees. If a tube of water with plate glass ends be placed within a coil of wire through which an electric current is passing, and plane polarised light be transmitted through the tube, the plane of polarisation will be turned through an angle in the direction in which the current circulates, and this angle will be proportional to the current. Verdet showed that in the case of a transparent (para-) magnetic substance the rotation is in the opposite direction to that of the current.

The curious effect of a magnet upon the luminous discharge in a vacuum tube and the recent experiments of Dr. Kerr, may indicate other relations between light and electricity and magnetism.

Having thus very briefly referred to the principal phenomena of magnetism and electromagnetism, we may proceed to give a short explanation of the medium or mechanism by which Maxwell accounted for these phenomena and their mutual interdependence.

From the well-known laws of the propagation of light, Maxwell assumed “as a datum derived from a branch of science independent of that with which we have to deal, the existence of a pervading medium, of small but real density, capable of being set in motion, and of transmitting motion from, one part to another with great, but not infinite, velocity.” Inasmuch as this medium can transmit undulations with finite velocity, it follows that it possesses a property analogous to mass, so that its motion implies kinetic energy; in addition to elasticity, in virtue of which its deformation implies potential energy.

It is well known that if a body rotate about a fixed centre there will be a tension along any radius drawn in the plane of rotation. The form which the earth would assume under the action of gravity only, if there were no rotation, would be that of a sphere. The diurnal rotation tends to cause the polar axis to contract and the equatorial diameter to increase; and this action would go on indefinitely were it not that at a certain early stage it is balanced by the attraction of gravitation, and thus the earth assumes a nearly spherical form, in which the polar axis is shorter than the equatorial diameter.

Referring again to the case of the earth, it is demonstrable from the fundamental laws and principles of dynamics that if matter were conveyed from the equatorial regions to the poles, and there deposited so as to lengthen the polar axis at the expense of the equatorial diameter, the rate of rotation of the earth would be increased and the length of the day would be diminished; while if the earth became more oblate its velocity of rotation would diminish. In fact, if any body be in rotation, and be unacted upon by external forces, or if the forces acting upon it be such as not to affect its rotation, and if the system be altered in shape by internal stresses or otherwise, so that its moment of inertia about the axis of rotation is increased, the angular velocity will be diminished and, in the case of a sphere becoming an oblate spheroid, the velocity at the circumference will also be diminished, while if the moment of inertia be diminished, the reverse effect takes place.

How Maxwell supposed that any medium which can serve as the vehicle of magnetic force consists of a vast number of very small bodies or cells capable of rotation, and which we may consider to be spherical or nearly so when in their normal condition, until we have reason to believe them to be of some other form. When magnetic force is transmitted by the medium, these bodies are supposed to be set in rotation about the lines of magnetic force as axis, and with a velocity depending on the intensity of the force. For the sake of fixing our ideas he supposed the rotation to be in the direction in which a right-handed screw would turn if it advanced in the direction of the force. We thus have the magnetic field filled with “molecular vortices” all rotating in the same direction about the lines of magnetic force as axes. As we have seen, these vortices will tend to contract in the direction of their axes of rotation, and to expand at right angles to this direction, so that if initially they are elastic spheres, they will tend to become oblate spheroids like the earth. This tendency will involve a tension in the medium along the lines of force, these being the lines along which contraction tends to take place, and this will be accompanied by an equal pressure in every direction perpendicular to the lines of force, on account of the tendency of the vortices to expand equatorially.

Now suppose that we have a north magnetic pole and a south magnetic pole placed near to one another. Lines of force will proceed from the North pole, generally in curved lines, to the South pole. The space in the neighbourhood of the poles will be filled with molecular vortices, which will be most energetic along the line joining the poles, and the velocities of the vortices will diminish as we pass into weaker portions of the field. The tension along the lines of force, tending to draw the North and South poles together, affords sufficient explanation of the apparent attraction between the poles; the kinetic energy of the molecular vortices accounts for the potential energy of the separated poles, which we thus suppose to be really kinetic energy, though possessed by the medium between the apparently attracting bodies and not by the bodies themselves. (Perhaps all examples of so-called potential energy we shall some day find to be really kinetic energy possessed by a medium with the properties of which we have been hitherto unacquainted.) When the poles approach one another, the field which is occupied by the vortices is diminished in extent, and though the velocity of the vortices is increased, the whole energy of the field is diminished, and the difference is expended in work done upon the approaching magnets. If the poles are of equal strength, and can come absolutely to coincide, the field is destroyed, all the vortices come to rest, and the energy possessed by them is all expended in work done on the magnets.

If two like poles, north poles for example, be placed near to one another, the lines of force proceeding from the one, instead of going to the other, will be turned aside, and if the poles be of equal strength, a plane bisecting, at right angles, the line joining the poles, will separate the lines of force due to the one from those due to the other, so that no line will cut the plane (Fig. 10). The lines of force thus passing nearly parallel to one another, the pressure exerted by the molecular vortices in every direction at right angles to the lines of force will cause an apparent repulsion between the poles.

To account for the transmission of rotation in the same direction from one molecular vortex to the next. Maxwell supposed that there exists between them a number of extremely minute spherical bodies which roll, without sliding, in contact with the surfaces of the vortices.