Each of the two circuits constituting the oscillation transformer taken separately has a natural time period of oscillation; that is to say, if the electric charge in it is disturbed, it oscillates to and fro in a certain constant period like a pendulum and therefore with a certain frequency. If the circuits have the same frequency when separated they are said to be isochronous. If n stands for the natural frequency of each circuit, where n = p/2π the above equations show that when the two circuits are coupled together, oscillations set up in one circuit create oscillations of two frequencies in the secondary circuit. A mechanical analogue to the above electrical effect can be obtained as follows: Let a string be strung loosely between two fixed points, and from it let two other strings of equal length hang down at a certain distance apart, each of them having a weight at the bottom and forming a simple pendulum. If one pendulum is set in oscillation it will gradually impart this motion to the second, but in so doing it will bring itself to rest; in like manner the second pendulum being set in oscillation gives back its motion to the first. The graphic representation, therefore, of the motion of each pendulum would be a line as in fig. 4. Such a curve represents the effect in music known as beats, and can easily be shown to be due to the combined effect of two simple harmonic motions or simple periodic curves of different frequency superimposed. Accordingly, the effect of inductively coupling together two electrical circuits, each having capacity and inductance, is that if oscillations are started in one circuit, oscillations of two frequencies are found in the secondary circuit, the frequencies differing from one another and differing from the natural frequency of each circuit taken alone. This matter is of importance in connexion with wireless telegraphy (see [Telegraph]), as in apparatus for conducting it, oscillation transformers as above described, having two circuits in resonance with one another, are employed.
| Fig. 4. |
References.—J. A. Fleming, The Alternate Current Transformer (2 vols., London, 1900), containing a full history of the induction coil; id., Electric Wave Telegraphy (London, 1906), dealing in chap. i., with the construction of the induction coil and various forms of interrupter as well as with the theory of oscillation transformers; A. T. Hare, The Construction of Large Induction Coils (London, 1900); J. Trowbridge, “On the Induction Coil,” Phil. Mag. (1902), 3, p. 393; Lord Rayleigh, “On the Induction Coil,” Phil. Mag. (1901), 2, p. 581; J. E. Ives, “Contributions to the Study of the Induction Coil,” Physical Review (1902), vols. 14 and 15.
(J. A. F.)
[1] For a full history of the early development of the induction coil see J. A. Fleming, The Alternate Current Transformer, vol. ii., chap. i.
[2] See A. Oberbeck, Wied. Ann. (1895), 55, p. 623; V. F. R. Bjerknes, d. (1895), 55, p. 121, and (1891), 44, p. 74; and P. K. L. Drude, Ann. Phys. (1904), 13, p. 512.
INDULGENCE (Lat. indulgentia, indulgere, to grant, concede), in theology, a term defined by the official catechism of the Roman Catholic Church in England as “the remission of the temporal punishment which often remains due to sin after its guilt has been forgiven.” This remission may be either total (plenary) or partial, according to the terms of the Indulgence. Such remission was popularly called a pardon in the middle ages—a term which still survives, e.g. in Brittany.
The theory of Indulgences is based by theologians on the following texts: 2 Samuel (Vulgate, 2 Kings) xii. 14; Matt. xvi. 19 and xviii. 17, 18; 1 Cor. v. 4, 5; 2 Cor. ii. 6-11; but the practice itself is confessedly of later growth. As Bishop Fisher says in his Confutation of Luther, “in the early church, faith in Purgatory and in Indulgences was less necessary than now.... But in our days a great part of the people would rather cast off Christianity than submit to the rigour of the [ancient] canons: wherefore it is a most wholesome dispensation of the Holy Ghost that, after so great a lapse of time, the belief in purgatory and the practice of Indulgences have become generally received among the orthodox” (Confutatio, cap. xviii.; cf. Cardinal Caietan, Tract. XV. de Indulg. cap. i.). The nearest equivalent in the ancient Church was the local and temporary African practice of restoring lapsed Christians to communion at the intercession of confessors and prospective martyrs in prison. But such reconciliations differed from later Indulgences in at least one essential particular, since they brought no remission of ecclesiastical penance save in very exceptional cases. However, as the primitive practice of public penance for sins died out in the Church, there grew up a system of equivalent, or nominally equivalent, private penances. Just as many of the punishments enjoined by the Roman criminal code were gradually commuted by medieval legislators for pecuniary fines, so the years or months of fasting enjoined by the earlier ecclesiastical codes were commuted for proportionate fines, the recitation of a certain number of psalms, and the like. “Historically speaking, it is indisputable that the practice of Indulgences in the medieval church arose out of the authoritative remission, in exceptional cases, of a certain proportion of this canonical penalty.” At the same time, according to Catholic teaching, such Indulgence was not a mere permission to omit or postpone payment, but was in fact a discharge from the debt of temporal punishment which the sinner owed. The authority to grant such discharge was conceived to be included in the power of binding and loosing committed by Christ to His Church; and when in the course of time the vaguer theological conceptions of the first ages of Christianity assumed scientific form and shape at the hands of the Schoolmen, the doctrine came to prevail that this discharge of the sinner’s debt was made through an application to the offender of what was called the “Treasure of the Church” (Thurston, p. 315). “What, then, is meant by the ‘Treasure of the Church’?... It consists primarily and completely of the merit and satisfaction of Christ our Saviour. It includes also the superfluous merit and satisfaction of the Blessed Virgin and the Saints. What do we mean by the word ‘superfluous’? In one way, as I need not say, a saint has no superfluous merit. Whatever he has, he wants it all for himself, because, the more he merits on earth (by Christ’s grace) the greater is his glory in heaven. But, speaking of mere satisfaction for punishment due, there cannot be a doubt that some of the Saints have done more than was needed in justice to expiate the punishment due to their own sins.... It is this ‘superfluous’ expiation that accumulates in the Treasure of the Church” (Bp. of Newport, p. 166). It must be noted that this theory of the “Treasure” was not formulated until some time after Indulgences in the modern sense had become established in practice. The doctrine first appeared with Alexander of Hales (c. 1230) and was at once adopted by the leading schoolmen. Clement VI. formally confirmed it in 1350, and Pius VI. still more definitely in 1794.