631 important term is that of longest period. Hence, properly choosing the epoch, we write where 2wA T tan 2lTT = 27T7 T " RT Hence we see the current is diminished either by increasing 7 or increasing R, also that the moment of reversal of current is not coincident with that of no electromotive force, but occurs after that time by an amount depending on the relative magnitudes of y and R. This explains in a general way what is known as the lead of the brushes in a continuous current machine. If we wished to apply a commutator to the Siemens alternate current machine for the purpose of producing an external current constant in direction, the change effected by the commutator should occur at an epoch after that of greatest electromotive force, an epoch which, with varying external resistance or varying speed, will depend on the resistance and speed. The power of the current is R.r 2 , and the energy in any consider able time, 0, is 0R 2vr 2 A 2 T a which shows that most power will be required to drive the machine when In what precedes it has been assumed that the copper wires are the only conducting bodies moving in the magnetic field. In most cases the moving wire coils of these machines have iron cores, the iron being in some cases solid, in others more or less divided. It is found that if such machines are run on open circuit the iron becomes hot, very much hotter than when the circuit of the copper wire is closed; in some cases the phenomenon is so marked that the machine actually takes more to drive it when the circuit is quite open than when the machine is short-circuited. The explanation is that on open circuit currents are induced in the iron cores, but that when the copper coils are closed the current in the latter by its induction diminishes the current in the iron. The effect of currents in the iron cores is not alone to waste energy and heat the machine ; the current produced is also actually less for a given intensity of field and speed of revolution. The cure of the evil is to subdivide the moving iron as much as possible in directions perpendicular to those in which the current tends to circulate. Continuous or Direct Current Machines. It has been shown that to produce a continuous current a commutator is needed. If there is but a single wire in the armature, or if there are more than one, but all are under maximum electromotive force at the same time, the current outside the machine, though always in the same direction, will be far from uniform. This irregularity may be reduced to any extent by multiplying the wires of the armature, giving each its own connexion to the outer circuit, and so placing them that the electromotive force attains a maximum successively in the several circuits. A practically uniform electric current was first commercially produced with the ring armature of Pacinotti as perfected by Gramme. Suppose a straight bar electromagnet surrounded by a coil of copper wire from end to end. Let the electromagnet be bent with the copper wire upon it until its ends meet and it forms an annulus or anchor ring. Let the two ends of the copper wire be connected, so that the iron core is surrounded by an endless copper wire, and you have the Pacinotti or Gramme ring. This ring rotates about its axis of figure between two diametrically opposed magnetic poles of opposite name. The ring may at any instant be supposed divided in halves by a diameter perpendicular to the diameter joining the centre of the poles. Equal and opposite electromotive forces act on the copper wire of the two halves, giving two opposite electric poles half way between the magnetic poles. If electric connexions could be maintained with these two points as the ring revolves, a continuous current would be drawn off. In practice this is only approximated to. The copper wire is divided into a series of equal sections, and at the point of junction of each section with its neighbour a connexion is made with a plate of a commutator, having as many divisions as there are divisions of the copper coil. Collecting, brushes bear upon the commutator plates, which are connected to the coil nearest to the point of maximum potential. Owing to the self-induction and mutual induction of the several coils of the armature, this point is displaced in the direction of rotation when a current is being drawn off, to an extent greater as the current is greater in relation to the strength of the magnetic field. The magnetic field in the Gramme and other continuous dynamo-electric machines may be produced in several ways. 1 Permanent magnets of steel may be used, as in the smaller machines now made, and in all the earlier machines ; these are frequently called magneto- machines. 2 Electromagnets, excited by a current from a smaller dynamo-electric machine, were introduced by Wilde ; these may be described shortly as dynamos with separate exciters. The plan of using the whole current from the armature of the machine itself for exciting the magnets was proposed almost simultaneously by Siemens, Wheatstone, and S. A. Varley. 3 For some purposes it is advantageous to divide the current from the armature, sending the greater part through the external circuit, and a smaller portion through the electromagnet, which is then of very much higher resistance, as the electromagnet is a shunt to the external circuit. Machines so arranged are sometimes called shunt dynamos. 4 The last two arrangements depend on residual magnetism to initiate the current, and below a certain speed of rotation give no practically useful electro motive force. In discussing the comparative efficiency of dynamo- machines there are two points to be examined (1) how much of the power applied is converted into energy of current in the whole circuit, whether external or in the wires of the armature or of the electromagnets, and (2) how much of the power is available outside of the machine. The 1 See for descriptions of various continuous current machines : BALL : Engineer, Hi. 307 ; Tel. Jour., ix. 415 ; Electrician, vii. 395 ; Engineering, xxxiii. 52. BRUSH: Engineering, xxxi. 55, 85,123; Engineer, xlv. 447, li. 15 ; Tel. Jour., vii. 21 ; Electrician, iii. 87 ; Shoolbred, 21 ; Fontaine, 181. BCRGIN : Engineering, xxxii. 205 ; Electrician, vii. 229. CANCE : Tel. Jour., viii. 346. DE MERITENS : Engineering, xxxii. 356, 380, 392. EDISON : Engineering, xxxii. 409, 418, xxxiii. 226, 252, 305, 407 ; Tel. Jour., x. 440 ; Engineer, Iii. 325, liii. 42 ; Electrician, viii. 28, 202. FEIN : Electrician, vii. 117; Engineering, xxxiii. 115. FITZGERALD: Engineer, 1. 284; Electrician, v. 224. GRAMME : Engineering, xxviii. 64, xxxiii. 58 ; Engineer, xlv. 447; Tel. Jour., vi. 491; Electrician, i. 15; Shool bred, 18 ; Fontaine, 151 ; Report from the Select Committee on Electric Lighting, 226; Schellen, 113. GULCHER: Engineer, Hi. 343; Electri cian, vii. 373. HEINRICH: Engineering, xxxii. 120 ; Tel. Jour., xviii. 359. HENLEY: Tel. Jour., ix. 288. JURGENSEN: Engineering, xxxiii. 130 ; Engineer, Hi. 237; Electrician, vii. 331. LADD: Fontaine, 124. LONTIN: Fontaine, 169. MAXIM: Engineering, xxxi. 618; Electri- cian, viii. 228; Tel. Jour., viii. 413. PACINOTTI: Engineering, xxxii. 501 ; Engineer, Hi. 293; Tel. Jour., vii. 217, ix. 478 ; Scheilen, 79; Xuovo Cimento, xix. (1864) ; Journal de Physique, x. 461. SCHUCKERT: Schellen, 139 ; Engineering, xxxiii. 244 ; Tel. Jour., vii. 119. SIEMENS: Engineering, xxviii. 101; Electrician, ii. 39, vii. 58; Shoolbred, 17; Fontaine, 173; Schellen, 42, 144. WALLACE- FARMER: Engineer, xlv. 447; Shoolbred, 20; Report from the Select Committee on Electric Lighting, 246. WESTON: Engineering, xxxii. 42 ; Electri cian, i. 267; viii. 230. WILDE: Shoolbred, 19 ; Fontaine, 121; Schellen, 49. 2 Mascart, Journal de Physique, vi. vii. 3 See for experiments on machines so arranged : AUERBACH and MEYER: Wiedemaim s Annalen, November 1879. CROMPTON: En gineering, xxxii. 205. HOPKINSON: Proc. Inst. Mech. E., 1879, 238, 1880, 266; Engineering, xxvii. 403, xxix. 424; Engineer, xlvii. 349; Tel. Jour., vii. 16 7, 185, viii. 167; Electrician, ii. 279, iv. 295. SCITWENDLER: Tel. Jour., vii. 47, 82, 395; Electrician, ii. 107, 117. 4 For experiments on " shuut dynamos " see Siemens, Trans. Roy. Soc., 1880.
