ELECTRICITY. 761 ELECTRICITY. magrnetic system, other units liave been adopted lor practicil use. (Sec Electrkwl Units.) The 'ampere' (q.v.), or practiial unit of cur- rent, is one-tenth the C. U. S. eU'itro-majinetie iinit: the 'ohm,' or practical unit of resistance, is substantially 10" C. ti. S. electro-magnetic units; the "volt," or practical unit of electro-mo- tive force, is substantially 10* C. G. S. electro- magnetic units. IxntcED Electric Currents. If the majmetic field inclosed by any conductor, e.g. a wire bent into a closed circle, is varied in any way, there will be prodvieed in the conductor an electric cur- rent, which continues only while the change goes on. This is called an "induced current.' and it is said to be due to an induced E. M. F. If there was a current in the conductor originally it will be either increased or decreased, dejicnding upon the direction of the induced current. This last is in such a direction that by its electro-magnetic action it will oppose that change in the magnetic field which produces it. Thus, if the change is due to the approach of a magnet having its north pole foremost, the induced current will be such as to cause the repulsion of the north pole while, if the change is due to the removal of the north I>ole of the magnet the induced current will be in the opposite direction. The change in the mag- netic field may be due, also, to the approach or removal of electric currents, to the change in the intensity of neighboring currents, or to changes in the original current in the conductor itself. Special cases of this last kind are afforded when a conductor carrying a current is broken, and also when the broken parts are reunited, thus again starting the current. In the former case the magnetic field starts at once to decrease: and owing to this there w ill be an induced current tending to neutralize the change in the magnetic field, i.e. in the same direction as the original current : this is sliown by the spark which passes between the ends of the conductor where the cir- cuit is broken. (This "extra current on breaking' is used often to produce a shock in the muscles of the arms or body: for. by increasing the magnetic field of the original current by winding the wire in a helix, a powerful shock may be felt.) When the circuit is again made, if the current regained its original value at once there would l)e a sudden increase in the magnetic field; as the field increases, however, there are induced evirrents tending to oppose the change, and hence the current regains its former value at a rate de- pending on the self-induction and the electrical resistance of the conductor — a very short time, however, in general is required. In all cases the induced E. M. F. (and therefore the intensity of the induced current) varies directly as the change in the tubes of magnetic induction, and inversely as the time taken in which to accomplish this change. The induced E. ^I. F. equals the change in the number of tubes of imluction in one second. In fact, the simplest way of defining a unit of self or mutual induction — or 'miit induction' — is to say that it is the induction in a circuit when the induced E. ^f. F. in it has the value one, while the inducing current varies at the rate of one unit per second. For. if M is the coelTicient of mutual induction between two coils, and if a current i passes through one. there are Mi tubes through the other; therefore, if the current i varies at the rate of one per second. Mi' will vary at the rate of M per second ; but the induced E. M. F. equals the rate of variation of Mi. i.e. equals M ; so, if the induced E. M. F. is unity, M nuist equal one. The energy required to produce the current comes from whatever agency cliangcs the mag- netic field, except when a current is made or broken, i.e. except cases involving self-induction. On breaking a circuit which carries a current, the cell or other source of E. il. F. ceases to furnish energy; and that re(iuired for the 'extra current' comes from the surrounding medium ; .so this current continues only so long as this supply lasts. This energy of the medium is associated with the magnetic field around the conductor due to the current. Similarly, when a current is "made' by joining the two ends of the broken conductor, the cell or source of E. M. F. begins to furnish energy; and this is spent in two ways at first, producing the magnetic field, and in over- coming the resistance of the conductor. When the current rises to its full value, as given by Ohm's law. the magnetic field reaches its final value, and all the energy now goes to overcoming the resistance (i-R?)- This energy of a mag- netic field — around either a crurrent or a jier- mancnt magnet — is undoubtedly kinetic; the ether and the portions of matter, if they are magnetic, are in motion. Clerk Maxwell ha.s shown how magnetic actions can be explained if a line of magnetic force is a linear vortex, the ether and the very small portions of matter spin- ning around this line as an axis, and if these difTerent vortices are made to depend on one' another by means of some kind of mechanism connecting them. The applications of induced currents are al- most too numerous to mention: earth inductors to measure the direction and intensity of the earth's magnetic field; induction coils to produce sparks, etc. ; transformers as used commercially to reduce or increase the E. M. F. of currents; all forms of dynamos: the telephone; all apparatus that depends upon the use of alternating cur- rents, etc. Alterxatixg Cckhexts akd Electrical Waves Along Condvctors. If the E. M. F. impressed upon a conducting circuit is not constant, the current will vary and there will be complications owing to the induced currents. In particular, if the E. M. F. is periodic in the same way that the motion of a pendulum is periodic, i.e. if it rises to a maximum, decreases to zero, becomes nega- tive, reaches a maximum negative value, increases to z.ero, then to its positive maxininm, etc.. ac- cording to the formula E=EVos jtt, the E. M. F. and the current are the simplest cases of 'alter- nating' electro-motive forces and currents. E" is the maximum E. !M. F., and the number of times the E. M. F. makes a complete period in one second is p/2Tr i where ir = 3.14150) . If the con- ductor to which this alternating E. M. F. is ap- plied is not too long, the intensity of the current in all parts of it will he the same at any one time: but. if the conductor is many miles long — • like an ocean cable, or a telephone or telegraph line over long distances — the E. Jl. F. and the intensity of the current will vary from point to point in such a way that there is a wave of V). M. F. and of current in the conductor. (These facts are perfectly analogous to the phenomena ob.served on shaking sidewise periodically one end of a short rope or of a long stretched rope.) The rate of transmission of the electrical waves along the conductor depends upon the properties of the
