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section. From the way in which the armature rotates these wires do not cut the lines of force; and thus induced 'eddy-currents,' a cause of waste of energy, do not occur as would be the case were the core solid.
Round this core is wound the insulated copper wire that forms the coil in which the E.M.F.s are induced. This wire —it must be carefully noted— is continuous; and herein we have .a great difference between this Clark or Siemens
kind of armature and that of In the upper part of fig. ii. we see this wire as it is actually wound ; and in the lower part of the figure there are shown a few sections of the coil, to indicate the mode pf winding.
This wire is, as we said, continuous. But at regular and close intervals the wire is brought out, is laid bare of insulating material, is soldered to an insulated copper segment m n (a few only of these copper segments are given in the figure), and is then led back to continue the winding. From what we have said it is clear that we have a continuous wire with which we can, by means of the insulated segments m n, &c., make metallic contact at regular and frequent intervals all round the ring. These segments are arranged all round the axle, and it is with them that the brushes of the external circuit make contact. In fig. ii. O represents the solid body of the axle; it is made of hard wood or other insulating material, there being an inner core of metal, insulated from the segments m n, to give necessary strength.
§ 9. The Gramme. The E.M.F.s Induced in the King.—Let us now consider the condition of this ring-armature, with its continuous wire, when it is rotated between the poles a b of the magnet; and let us at present suppose that there are no springs or brushes in contact with the segments. Were it not for the core, the magnetic field would consist of lines of force running nearly straight across from one pole-piece to the other. These lines would pierce the coils of the armature, the number piercing each coil depending upon the position of that coil. Thus, a coil which is at the top of the ring depicted in § 8, fig. i., or which is situated equatorially, embraces the maximum of lines, supposing the field to be uniform. As the ring turns, this coil embraces fewer and fewer, until, when it lies edgeways to the lines or is situated 'axially,' it embraces none. (If the field be not uniform this statement must be modified; but, in any case, the coil embraces zero lines when situated axially.) As the ring turns still further, our coil begins to embrace lines in the other direction; and these reach a maximum when it is at the bottom of the ring, i.e. when it is again situated equatorially, 1800 from its initial position. All this will give an induced E.M.F. in one direction, as has been already explained in Chapter XXII. § 4, and elsewhere. As the coil turns through the other 1800 back to its initial position, there will, it is clear, be induced an E.M.F. in the opposite direction.
Thus, as the ring rotates, all the coils that are to the one side of the equatorial diameter give an E.M.F. in the one direction, and all those lying to the other side give an equal E.M.F. in the opposite direction. The result will be that no current will flow, but that the different parts of the wire, and so also the copper segments connected with them, respectively, will be maintained at different potentials. Thus, in the figure here given we shall have
Fig. i. Fig. ii.
the wire at A and B, i.e. at the extremities of the equatorial diameter, maintained at the greatest SV, the potential falling from (siy) A symmetrically along the wire, through each route, down to B.
Thus, though the individual coils assume all positions in turn, the ring, as a whole, maintains a character that is constant as long as there is constant field-strength and velocity of rotation. The revolving ring has been not inaptly compared to a stationary system of two equal batteries (see fig. ii.) set against one another; these batteries giving no current in their circuit, but maintaining the poles A and B at a constant SV. We can evidently obtain a current in an external circuit by connecting A and B.
The core.—We have hardly mentioned the core in what we have said. The fact is that the core only modifies the field; its presence does not affect the general theory of the ring as given above. Its action is mainly to concentrate the field upon the coils. The lines of force cannot now, to any considerable extent, get across the space inside the ring; they follow the core through the coils. The presence of the core does not affect the two main facts: (1) that when the coils lie axially they cut no lines of force; and (2) that the change in direction of the E.M.F. occurs as the coils pass the equatorial position.
It is found that the soft iron wire changes its magnetism in a time that is practically inappreciable; and hence we can, if we like, regard the core as stationary, and the coils as slipping round upon it.
(For a modification of the sense in which axially and equatorially must be used when a current is running, see § 12.)
§ 10. The Gramme. The Collecting Brushes—As in the analogous case of the two opposed batteries, represented in § 9, fig. ii., so, in the case of the gramme-ring represented in fig. i., we can obtain a current if we connect the parts A and B.
We have explained in § 8 how the wire that forms the coil is, at a series of points all round the ring, connected with insulated copper segments that are fixed in the axis on which the ring turns. If, then, there be metallic springs or brushes formed of wire, pressing against the axis at the extremities of the equatorial diameter of the same, these will practically be in contact with each segment of the wire coil in turn as it arrives at the positions A or B. In the Gramme machine these collectors are brushes of metallic wire. However great the speed of revolution, these brushes will never be jerked away from contact, as might a single spring; and with them it is easier to have contact always with two consecutive segments at once, and thus insure a current that is continuous, even though undulatory. The wires of the external circuit are, of course, attached to these collectors. The two halves of the ring then combine, as would the two batteries acting 'parallel,' to send a current through the external circuit.
§ n. Curve of Potential Round the Collecting Axis.—Let us suppose the brushes to be detached, and the potential at different positions round the axis to be examined. This may be done by employing a quadrant electrometer, of which one pair of quadrants are to earth, and the other pair connected with an insulated wire brush ; this brush is applied to the axis at different points in succession.
We find a fall or rise in potential from segment to segment as we move from A to B or from B to A; this fall, in properly constructed machines, occurring symmetrically down both halves of the axis.
This fall in potential is, of course, discontinuous, since the segments are limited in number. But when the segments are very numerous the fall in potential round the collecting axis can be represented approximately /'' ~x\ by a continuous curve. / '* \
In the accompanying diagram, the shaded I circle represents a section of the axis; the dark \ dots on this circle represent sections of the in-' sulated copper segments; and the larger dotted curve represents the fall in potential from the upper extremity A of the equatorial diameter, both ways, round to the lower extremity B of the same. If we draw a radius from the centre of the axis, through the dot representing any particular segment, to meet the outer curve, then the intercept between this dot and the outer curve represents in magnitude the relative potential of the segment in question. (This will indicate to the reader how the outer 'curve of potential' is plotted out.)
In a good machine this fall of potential should be regular, The brushes should be in contact with the axis at the points of maximum and minimum potential respectively. We shall find, however, that, as soon as a current runs, these positions of maximum and minimum potential shift round the axis.
§ 12. The ' Lead' that Occurs when a Current is Running-.—
First, let us suppose that the ring is revolving, but that, the external circuit being not yet completed, there is no current flowing. The two halves of the ring act merely to maintain two points, e.g. A and B, at a certain maximum AV. If the lines of force (see § 9, fig. i.) run straight across in what we have called ai axial direction, then A and B will lie equatorially as shown. If, however, the core of the ring take an appreciable time to gain and lose its magnetism, the lines of force, and so also the line A B joining the points of maximum AV, will be shifted round to a greater or less extent. This question can be tested directly by experiment. A brush makes contact with the axis at different points in succession round its circumference. An insulated wire