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.

§ 11. 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 segnients are very numerous the fall in potential round the collecting axis can be represented approximately by a continuous curve.

B

In the accompanying diagram, the shaded circle represents a section of the axis; the dark dots on this circle represent sections of the insulated 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 an 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

connects this brush with one pair of quadrants of an electrometer, the other pair of quadrants being to earth. It is stated that when the positions A and B of maximum and minimum potential are thus tested, the line A B is found to be practically equatorial, or lies at right angles to the line joining the poles of the field-magnets, whatever be the speed of revolution of the ring. Hence we conclude that the core of the ring does not take any appreciable time to change its magnetism as it rotates.

This view is supported by S. P. Thompson and others; but there are some who are not satisfied of its truth.

Secondly, let us suppose that the brushes are attached and that an external current is running. If the direction of the current be followed, according to the principles explained in Chapter XXI., it will be seen that (see § 9, fig. i.) the currents in the two halves of the ring both act to make the core of a N polarity at B, and of a S polarity at A. Now the field-magnets tend to make the core of a N polarity at N' opposite to S, and of a S polarity at S' opposite to N. Hence, on the whole the core will acquire a N polarity at some point between N' and B, and a S polarity at some point between S' and A, opposite to the former. The effect will be as if the polarity of the core were shifted on in the direction of movement of the ring. Hence the line A B, of the points of highest and lowest potential, will also be shifted on through an equal angle. And therefore the brushes must also be shifted on.

This shifting on of the brushes in the direction of rotation is called 'Lead.

According to the above view, which is supported by experiments on the part of S. P. Thompson and others, the amount of lead depends upon the ratio between the field-strength due to the field-magnets, and the inductive action upon the core of the current in the ring. It does not depend upon velocity of rotation, provided that the current is constant; whereas, were 'lead' due to residual magnetism in the core, the amount of this lead would depend upon the velocity of rotation though the current were constant.

§ 13. Armatures Wound for E.M.F.' and 'for Current.'As with batteries, so with armatures; we can construct them either to give a high E.M.F., regardless of the resistance thereby unavoidably introduced, or to give a low resistance, thereby sacri

ficing E.M.F.

All depends upon the nature of the external circuit (see Chapter XIII. §§ 6 and 13).

For high E.M.F. we must have many turns of wire; and therefore it must be long and fine, or of high resistance.

For low internal resistance we must have few turns, and thick wire. Having few turns, we have low E.M.F. (see § 2).

Sometimes there are on the same ring, or on parallel rings, two coils, these being capable of being joined either in series or in parallel circuit.

§ 14. The Siemens-Alteneck Armature. As we have stated in Chapter XXI. § 8, the origin of the induced E. M. F. must doubtless be sought for in the cutting of the lines of force by the wire of the coil. Now since, as can be experimentally shown, there are hardly any lines of force that find their way across the inside of the ring, it follows that the wire lying on the inside of the ring is not cutting any lines, and is therefore passive as regards the productiveness of an E.M.F. It is simply a dead resistance. In the Siemens-Alteneck machine a drum replaces the ring, and the wire is wound over this, there being therefore no wire, saving at the ends of the drum, that does not cut lines of force. The long shape of the drum further renders smaller the proportion of the idle wire at the ends.

§ 15. The Brush Machine. On a very different principle is constructed the 'Brush' machine; the name being after that of the inventors. The theory of this machine is so complicated that we cannot give it here clearly and yet briefly. We therefore refer the reader to S P. Thompson's work on 'Dynamo-Electric Machinery' (Spon & Co., London).

This machine gives very high E.M.F.s, and is therefore used where such are required.

§ 16. Magneto Machines.We will now discuss very briefly the four most important types of machines, beginning with the 'magneto machine' as the oldest and simplest form. The accompanying figure represents diagrammatically the typical magneto.' In this form, of which the machine shown in fig. i. of § 8 was an example, the field is given by a permanent steel magnet. Such fields are very constant, and therefore the E.M.F. of the current will vary simply with the velocity of rotation. For purposes of demonstration and explanation of the theory of dynamos, such a

property is very useful.

Hence the magneto is much used for teaching purposes. The same property, coupled with the easy

S

regulation of the field by means

of a keeper (see § 3), makes the magneto useful also for medical purposes. But in the arts and in commercial undertakings it is never used, as being relatively feeble for its mass as compared with any of the electro-magnet forms.

Magnetos cannot be made with certainty to be of the same E.M.F. We can therefore couple them in series only, such a series of magnetos acting like one machine of the sum of their E.M.F.s and of the sum of their resistances. We cannot couple them parallel, or 'for current,' for the machine of lower E.M.F. might serve only as a branch circuit through which the other machine was driving a current. It would

act as a 'motor' (see Chapter XXIV.) and not as a driver of current. We may add that when a magneto is run at constant speed its E.M.F. is constant. Hence, in calculations we may deal with such as if they were voltaic batteries of constant E.M.F.

§ 17. Separately-Excited Machines.—When the field-magnets are electro-magnets, excited by a current from an independent source, we have what is called a separately-excited machine. This form differs very little in principle from a magneto, but the field is much stronger, and we can vary its strength within very wide limits. Hence we have great control over the E.M.F.

Such machines can be used in series or in parallel circuit.

An obvious disadvantage of this form is that we require a separate source of current. Neither the magneto nor the separately-excited machine can be constructed so as to be self-regulating, whereas we shall see that some other forms can be so constructed, these forms being compound.