40 ELECTRICITY [ELECTRIC CURRENT. Max- well s theory. Hopkin- son s exjxiri- ments. longer. He suggests that the same thing may be true of elastic recovery. He does not allude to the fact (possibly he was uuware of it) that two residual charges of different sign may be superposed and reappear separately, although the possibility of this is to a certain extent involved in his remark. The analogous elastic phenomenon has recently been observed by F. Kohlrausch. Maxwell 1 has shown that phenomena exactly like the residual discharge would be caused by conduction in a hete rogeneous dielectric, each constituent of which by itself has not the power of producing any such phenomenon, so that the phenomenon in general might be due to " heterogeneity " simply. Hopkinson has lately made experiments on the residual discharge of glass jars. He observed the superposition of residual charges of opposite signs, and he suggests theories analogous to those of Kohlrausch and Maxwell. He finds that his results cannot be represented by the sum of two simple exponential functions of the time, and concludes, therefore, that heterogeneity must be an important factor in the cause of the phenomenon. The polarities of the different silicates of which the glass is composed rise or decay with the time at different rates, so that during insulation the difference of potential between the armatures E would be represented by a series 2^ A r e ~ ^ rt If, therefore, we charge a jar positively for a long time, and then negatively for a shorter time, the second charge will reverse the more rapidly changing polarities, while the sign of the more sluggish will not be changed ; when, therefore, the jar is discharged and insulated, the first- mentioned polarities will decay more quickly at first and liberate a negative charge, and, finally, as the more sluggish also die away, a positive charge will be set free. Hopkinson also made the impor tant observation that agitation of the glass by tapping accelerates the return of the residual discharge. ON THE PASSAGE OF ELECTRICITY THROUGH BODIES. We have hitherto supposed electricity to be either immovably associated with perfectly non-conducting matter, or collected on the bounding surfaces of conducting and non-conducting media in such a way that the force tend ing to cause it to move is balanced by an invincible resist- Electric ance. We have now to consider what happens when there currents, is a finite unbalanced resultant force at any point in a conducting medium. If a conducting sphere of radius a be charged with Q units of positive electricity, its potential will be . Connect this sphere by a long thin wire, whose capacity may be neglected, with another uncharged sphere of radius b, then we know that the potentials of the two spheres become equal; and since what we call electricity is subject to the law of continuity, the whole charge on the two spheres must be the same as before. Hence if U be the common potential, we must have U = , . It ap pears, therefore, that the potential of a has fallen by , - , and an amount - Q of positive electricity has passed from a to b, and also a -- rth part of the (t ~T- electric potential energy has disappeared. In accordance with our hypothesis that electricity obeys the law of con tinuity like an incompressible fluid, we explain this transference of electricity by saying that an electric cur rent has flowed through the wire from the place of higher to the place of lower potential. We define the intensity or strength C of the current as the quantity of electricity which crosses any section of the wire in unit of time. Owing to the law of continuity the current intensity is of course the same at every point of a linear conductor. Electricity and Magnetism, 327 sqq. In the case which we have just given, the whole transference takes place in so short a time that we cannot study the phenomenon in detail. It is obvious that C will vary rapidly from a large initial value, when the difference between the potentials of the spheres is , to zero when they are at equal potentials. It is possible, by replacing the wire by wetted string or other bad conductor, to prolong the duration of the phenomenon to any extent, so that C should vary very slowly ; and we can imagine cases where C would remain constant for a long time. Machines for producing a continuous or " steady " current have been invented in considerable variety, the first of the kind having been the Pile of Volta. Of such machines we shall have more to say when we come to discuss Electro motive Force. We have seen, in the case of our spheres, that the passage of the electric current was accompanied by a loss of potential energy. The question thus arises, Appli< what becomes of the energy after the current dies away, ^ono! and the equalization of potential is complete ] This leads ^ "! us to look for transformations of energy depending on the vation electric current, or, in other words, to look for dynamical energj effects of various kinds due to it. Accordingly we find the passage of the electric current accompanied by magnetic phenomena, sparks, heating of the circuit, chemical decom positions, mechanical effects, &c. All these are observed in the discharge of the Leyden jar and other electrostatic reservoirs of potential energy. Exactly similar effects, some more, others less powerful, are observed accompany ing the current of the voltaic battery and other machines which furnish a steady flow of electricity. In all such cases we have (1) a source of energy, (2) a flux of electricity, (3) an evolution of energy in different parts of the circuit. We reserve the consideration of (1) for the present, as being the most difficult, and devote our attention to (2) and (3). Ohm s Law applied to Metallic Conductors. We have already seen how to measure the strength of Measu an electric current in a linear conductor. According to ment < the definition we gave above, the unit current strength Cl1 would be that for which a unit of electricity passes each section of the conductor in unit of time. If the unit of electricity is the electrostatic unit, this is called the electro- statical unit of current. We have supposed above that the current consists in the transfer of a certain amount of + electricity in a certain direction, which we shall call the positive direction of the current, and this for most purposes is convenient. We must remember, however, that no dis tinction can be drawn between the transference of + Q units of electricity in one direction and the transference of Q units in the opposite direction ; for we have no experimental evidence on which such a distinction can be founded. We may measure the current by any one of its various Electn effects. The method most commonly used, both for indi- magne eating and measuiing currents, is to employ the mag- TTiea8U1 netic effect. According to Oersted s discovery, a magnetic north pole placed in the neighbourhood of a stiaighf current is acted on by a force such that, if the pole were to continually follow the direction of the force, it would describe a circle round the current as an axis, the direction of rotation being that of the rotation of a right handed cork-screw which is traversing a cork in the positive direction of the current. If, therefore, we have currents of different strength in the same wire, the force exerted on a magnet which always occupies the same position relatively to the wire will be a measure of the current. The force exerted on the magnet may be found by balan cing it against known forces, or by allowing the magnet to
oscillate under it and finding the time of oscillation. It