loses a negative charge, while it is able to retain a positive charge

under these conditions.

When a brush discharge is formed at a point the potential will be greater if the point is positively electrified than if it is negatively electrified.

The most striking difference is obtained if a discharge is produced between a charged conductor and the surface of a non-conductor on the surface of which some badly conducting powder, such as lycopodium, has been strewn, or on to the surface of a photographic dry-plate. The appearance when the conductor is positively electrified is shown in Fig. 543, while in Fig. 544 the appearance when the conductor is negatively electrified is given, and it will be seen that the difference is most marked. The explanation of these differences has not yet been given, and although there are many other facts which seem to have a bearing on this most fascinating branch of physics, space will not permit of our dealing with them in these pages. The reader who wishes to pursue the subject further will find a very complete account of the work which has been done in this subject in Professor J. J. Thomson's "Recent Researches

in Electricity and Magnetism,"

PART IX.-MAXWELL'S ELECTRO

MAGNETIC THEORY

CHAPTER XIX

TRANSFERENCE OF ELECTRO-MAGNETIC ENERGY AND MAXWELL'S ELECTRO-MAGNETIC THEORY OF light

569. Poynting's Theory.-We have seen how, according to the views of Faraday and Maxwell, if F is the strength of the electrostatic field at a given point, and K the specific inductive capacity of the medium, the energy stored up in each unit of volume of the dielectric at the given point is equal to KF2/8′′. It can also be shown that in the same way the energy stored up in each unit of volume of a medium of which the permeability is μ at a point of a magnetic field where the strength of the field is H, is equal to μH28. Hence the electric and magnetic energy per unit volume of a medium, which is the seat of both electro-static and magnetic forces, is KF2/8π+μH2/8π.

Suppose a condenser, AB, Fig. 545, is charged so that the plate A is positive, then tubes of force will stretch from the plate A to the plate E.

medium, since there is no electro-magnetic force produced in the medium. If the plates of the condenser are connected by a conducting wire, which we may suppose of very great resistance, so that the condenser takes an appreciable time to discharge, this wire will be traversed by an electric

current, and at the same time the difference of potential between the plates of the condenser will diminish. During the passage of the electricity through the wire, there will be produced an electro-magnetic field in its neighbourhood, that is, the surrounding medium will possess energy due to the magnetic strain set up. Also the passage of the electricity will be accompanied by the production of heat in the wire, according to Joule's law. When the discharge is complete, the whole of the energy which was originally stored up as electro-static strain of the medium between the plates of the condenser will have been converted into heat in the connecting wire. During the process, however, a certain proportion will have existed in the medium surrounding the wire in the form of energy of the magnetic field, although it also finally becomes changed into heat in the wire. An interesting question now arises as to the way in which the energy travels from the medium between the plates to the wire. Poynting has shown that the energy travels through the medium separating the plates and surrounding the wire, and that the paths along which the energy moves are the intersection of the equipotential surfaces of the electro-static and the electro-magnetic fields. Thus in the case of the condenser discharging through the wire, the tubes of force are supposed to spread out from the space between the plates, the ends of the tubes remaining on the plates. These tubes will meet the wire, and when they do this, they will be broken up and the energy which each contained will be delivered to the wire, where it will appear as heat. The breaking up, or rather absorption, of each tube by the wire will allow another tube to expand from the space between the plates. For each tube, since it exerts a lateral compression on the inside tubes, will tend to prevent their leaving the space between the plates. The absorption of a tube by the wire will reduce this lateral pressure exerted on the inside tubes, and hence more tubes will be able to swell out from the space between the plates.

On Poynting's theory the energy which is transmitted, say, along a telegraph cable is not transmitted along the conducting wire but through the insulating sheath, the object of the wire being to direct the path along which the energy travels.

The telegraph cable may be regarded as a wire surrounded by a concentric conductor, the sheath, the interspace being filled with a dielectric. When the wire is positively electrified and the sheath negatively by connecting the wire, say, to the positive plate of a charged condenser, the negative plate being put to earth, that is, connected to the sheath, tubes of force will stretch across from the wire to the sheath. These tubes will travel forward, each carrying its share of electrical energy. If we suppose the thickness of the insulating covering to remain the same throughout, then the length of the tubes of force will remain the same as they travel onward. The difference of potential between the ends of each tube will, however, diminish as the tube advances, according to

Ohm's law. Since the difference of potential between the wire and the sheath decreases, the work which would have to be done to carry unit charge from the neighbourhood of the wire to that of the sheath will decrease, and since the distance between the two is supposed to remain the same, it must follow that the force acting on the unit charge will also diminish, that is, the strength of the field, F, between the wire and the sheath will decrease as we go from the sending end of the cable. Now we have seen that the energy contained in unit length of each tube of force is equal to F/2. Hence, since the length of the tubes remains constant and decreases, the quantity of energy contained in each tube will decrease as the tube travels away from its starting-point. The passage of the current through the wire and sheath is, we know, accompanied by the conversion of a certain proportion of electrical energy into heat, and this decrease in the electrical energy of each tube as it travels along represents the loss of energy in the conductor, according to Joule's law.

Since the electro-static lines of force are radial, the electro-static equipotential surfaces will be cylinders which are concentric with the wire and the sheath. The magnetic lines of force are circles with the wire as centre and in planes at right angles to the length of the wire, so that the magnetic equipotential surfaces are planes which pass through the wire. The intersection of the two sets of equipotential surfaces will be lines which are parallel to the axis of the wire, and it is along these lines that the energy travels out from the battery at the sending station to the distant end of the telegraph cable.

The supposition that the electro-static equipotential tubes are cylinders of which the axis of the wire is the axis is not quite true, for as we go away from the sending-point the difference of potential between the wire and the sheath will decrease by Ohm's law, so that the number of equipotential surfaces included between the wire and the sheath must decrease, the surfaces being supposed to be drawn for a given difference of potential between consecutive surfaces. The result is that the equipotential surfaces are really frustra of cones. These cones will intersect the wire and the sheath at intervals along the cable, and it is along the line of intersection of such a cone with the magnetic equipotential surfaces that the electrical energy travels which enters the wire or sheath and is converted into heat. If the wire and sheath were composed of conductors of zero resistance there would be no fall of potential along the wire, and in this case the electro-static equipotential surfaces would nowhere intersect either the wire or the sheath, so that no electrical energy would travel into the wire or sheath, and hence no heat would be generated.

When a current is flowing in a circuit, say a coil, the space surrounding the coil will be a magnetic field, and hence there will be a certain amount of energy stored up in this magnetic field. If now the current

is stopped the magnetic field will cease to exist, and the question arises, what becomes of the energy which was stored up in the field? This energy, if the circuit is at a distance from other circuits, returns to the circuit and gives rise to the induced current within the circuit which is produced when the current is stopped. Thus the phenomenon of selfinduction (§ 518) is due to the return to the circuit of the energy which during the passage of the current is stored up in the magnetic field produced by the current. When a current is started in a circuit, some of the energy of the battery employed to send the current is used up in providing the energy of the magnetic field. When a second circuit is near the circuit in which the current is flowing, on stopping this current some of the energy of the magnetic field will soak into this neighbouring circuit and will produce in it an induced current.

570. Magnetic Force caused by the Motion of Electro-static Tubes of Force.-We have seen that when electricity moves from one part of a conductor to another, that is, when a current passes through a conductor, that a magnetic field is produced in the neighbourhood of the conductor in which the electricity is moving. It might be conceived that the magnetic field produced in this way by the movement of electricity was due to some special property of the electricity when it is moving from one part of a conductor to another. When a conductor is charged with electricity, the electricity being at rest, the space surrounding the charged body is in such a condition that electro-static forces are set up, that is, it is an electro-static field. In the last section we have seen how the passage of an electric current through a wire, which for simplicity we took double so that the outgoing and return were close together (it must be remembered that there must always be a return; it may be at a considerable distance from the portion of the circuit we are immediately considering, but it is there nevertheless), is accompanied by the motion of the electro-static tubes of force through the medium between the wires. Since by the motion of electricity in a conductor which is accompanied by the motion of the tubes of electro-static force, or, as we may call them, the Faraday tubes, to distinguish them from the tubes of magnetic force, magnetic forces are set up in the dielectric surrounding the conductor, the question arises, would magnetic forces be set up in the same way in the surrounding dielectric if we were to cause the motion of Faraday tubes through the dielectric by moving the body on which a charge exists? Thus suppose we consider two metal plates placed parallel to one another in air, one charged positively and the other negatively. The Faraday tubes will then stretch across from the positive plate to the negative plate, and in the space between the plates we have an clectro-static field; but as long as the charges on the plates are at rest there will be no magnetic field. Suppose now the two plates are moved parallel to their own plane and at the same speed, then the tubes will not move with reference to the charged plates but they will swcep