574
DYNAMO
hundreds or thousands, but by hundreds of thousands. .dicular to the axis so as to produce an angiikr deflection S0, and let 0' be the corresponding lateral deviation at 0 . In hke manner, Yet the fundamental theory of the dynamo, as a machine in the reversed motion, let a small deflection 50 at 0 produce a for generating electromotive force, remains but little changed, and the advance since Faraday’s time may, by lateral deviation /3 at 0. The3 theorem (6) asserts that J - = JL . . . (8) comparison with his results, be regarded as a progressive 'Sd' 56’ ‘ improvement of the mechanical and electrical design or, in optical language, the “apparent distance ” ofOfrom O'is to leading to a fuller realization of the idea which was already that of 0' from 0 in the ratio of the refractive indices at 0 and 0 present in his mind. His experiments on the induction of "TntScond reciprocal theorem of Helmholtz the configuration currents in a coil of wire during the approach or recession O is slightly varied by a change 5qr m one of the co- of a magnet led naturally to the explanation of induced Helmordinates, the momenta being all unaltered, and dp, is electromotive force as caused by the linking or unlinking holtz’s the consequent variation in one of the momenta after second re- time T. Similarly in the reversed motion a change 5q s of magnetic lines of flux with an electric circuit. For the ciprocal pr0(juc'es after time r a change of momentum 5pr. The more definite case of the dynamo, however, we may, with theorem, theorem asserts that Faraday, make the transition from line-linkage to the 5p't:5qr=5pr:5q's . . • • (9) precisely equivalent conception of “line-cutting” as the This follows at once from (2) if we imagine all the 5p to vanish, and source of E.M.F.—in other words, to the idea of electric likewise all the 5q save 5qr, and if (further) we imagine all the Ap conductors “ cutting ” or intersecting1 the lines of flux in to vanish, and all the Aq' save Aq's. Reverting to the optical virtue of relative motion of the magnetic field and electric illustration, if F, F', be principal foci, we can infer that the convergence at F' of a parallel beam from F is to the convergence at * of circuit. On 28th October 1831 Faraday mounted a a parallel beam from F' in the inverse ratio of the refractive indices copper disc so that it could be rotated edgewise between at F' and F. This is equivalent to Gauss’s relation between the the poles of a permanent horse-shoe magnet. When so two principal focal lengths of an optical instrument. It may be rotated, it cut the lines of flux which passed transversely obtained otherwise as a particular case of (8). We have by no means exhausted the inferences to be drawn from through its upper half, and by means of two rubbing Lagrange’s formula. It may be noted that (6) includes as particular contacts, one on its periphery and the other on its spindle oases various important reciprocal relations in Optics and Acoustics or axis, the circuit was closed through a galvanometer, formulated by Clausius, Helmholtz, Thomson and Tait, and Lord which indicated the passage of a continuous current so Rayleigh. In applying the theorem care must be taken that m the reversed motion the reversal is complete, and extends to every long as the disc was rotated velocity in the system ; in particular, in a cyclic system the cyclic (Fig. 1). Thus by the invention of motions must be imagined to be reversed with the rest. Conthe first dynamo Faraday proved spicuous instances of the failure of the theorem through incomp e ® his idea that the E.M.F. induced reversal are afforded by the propagation of sound in a wind and through the interaction of a the propagation of light in a magnetic medium. It may be worth while to point out, however, that there is no magnetic field and an electric such limitation to the use of Lagrange’s formula (1). In apply- circuit was due to the passage ing it to cyclic systems, it is convenient to introduce conditions of a portion of the electric circuit Fig. 1. already laid down, viz., that the co-ordinates qr are the palpable co-ordinates, and that the cyclic momenta are invariable, bpeciai across the lines of flux, or vice inferences can then be drawn as before, but the interpretation versd, and so could be maintained if the cutting of the lines cannot be expressed so neatly owing to the non-reversibility o were made continuous.2 the motion. A dynamo, then, is a machine in which, by means of Authorities.—The most important and most accessible early continuous relative motion, an electrical conductor or system authorities are Lagrange, Ittcanique Analytique, 1st ed.. Pans, of conductors forming part of a circuit is caused to cut the 1788, 2nd ed., Paris, 1811 ; Hamilton, “On a General Method m Dynamics,” Phil. Trans., 1834 and 1835 ; Jacobi, Vorlesungenuber lines of a magnetic field or fields; the cutting of the Dynamik, Beilin, 1866, reprinted in Werke, Supp.-Bd., Berlin, magnetic flux induces an electromotive force in the 1884. An account of the extensive literature on the differential conductors, and when the circuit is closed a current flows, equations of dynamics and on the theory of variation of parameters whereby mechanical energy is converted into electrical is given by Cayley, ‘ ‘ Report on Theoretical Dynamics, Brit. Asm. Rep., 1857, Mathematical Papers, vol. in., Cambridge, 1890. lor energy. the modern developments reference may be made to Ihomson and Little practical use could be made of electrical energy so long Tait, Natural Philosophy, 1st ed., Oxford, 1867, 2nd ed Cam- as its only known sources were frictional machines and voltaic bridge, 1879 ; Lord Rayleigh, Theory of Sound, vol. i., 1st ed., batteries. The cost of the materials for producing electrical London, 1877, 2nd ed., London, 1894 ; Routh, Stability of Motion, currents on a large scale by chemical action was prohibitive, win e London, 1877, and Rigid Dynamics, 4th ed., London, 1884 ; Helm- the frictional machine only yielded very small currents at extremely holtz, “Ueber die physikalische Bedeutung des. Prmcips der hifdi potentials. In the dynamo, on the other hand, electrical kleinsten Action,” Crelle, vol. c. 1886, reprinted (with other in a convenient form could be cheaply and easily obtained nate papers) in Wiss. Abh. vol. iii., Leipzig, 1895 ; Larmor, On energy mechanical means, and with its invention the application o Least Action,” Proc. Land. Math. Soc. vol. xv. 1884. As to^ the by to a wide range of commercial purposes became economicquestion of stability, reference may be made to Poincare, bur electricity ally possible. As a converter of energy from one form to another lequilibre d’une masse fluide animeed’un mouvement derotation, is only surpassed in efficiency by another electrical appliance, Acta Math. vol. vii., 1885 ; Klein and Sommerfeld, Theorie des it the transformer (see Transformers)^ In this there is Kreisels, pts. 1, 2, Leipzig, 1897-98 ; Lioupanoff and Hadamard, namely, conversion of electrical energy at h high potential into Liouville, 5me serie, vol. iii., 1897. A remarkable interpretation merely electrical energy at a low potential, or vice versa, but m the dynamo of various dynamical principles is given by Hertz in his the mechanical energy which must be applied to maintain t ie posthumous work Die Prinzipicn der Mechanik, Leipzig, 1894, of relative movement of magnetic field and conductor is absorbed, and which an English translation appeared in 1900. (h. Lb.) reappears in an electrical form. A true transformation takes and the proportion which the rate of delivery of electric, Dynamo.—Invented by Faraday in 1831, the place, bears to the power absorbed, or in other words the efficiency, dynamo ranks with the telegraph and telephone among energy is the more remarkable. The useful return or “output at the the most striking achievements of science, and the ma- terminals of a large machine may amount to as much as 95 pe terial progress that marked the later years of the 19th cent, of the mechanical energy which forms the input. bm century was in no small measure due to the practical applica- it needs some prime mover to’drive it, the dynamo has not made any direct addition to our sources of energy, and does not thereioio tion of these three electrical inventions. Since 1830 rank with the primary battery or oil engine, or even the steam the simple model constructed by Faraday has been engine, all of which draw their energy more immediately irom gradually developed into the dynamos of 5000 horseExperimental Researches in Electricity, series ii. § 6, pars. • > power or more, which are constructed to meet the and series xxviii. § 34. needs of large cities for electric lighting and power, 259-60, 2 Ibid., series i. § 4, pars. 84-90. and the machines in use are to be numbered, not by
