mitrailleuse bullets, being constant for both directions of movement of the stream. This is not the case with low vacuum discharges.

(8) Rotation about a pole.-So also we can obtain rotations about the pole of a magnet; but, unlike the case of low vacuum discharges, this is independent of the direction of movement of the molecules.

(e) Action of molecular streams upon one another.--Dr. Crookes found that two streams running in the same direction side by side repel one another; they appear to behave as mutually repelling similarly charged particles, not as parallel currents.

Note.—It has been supposed that two similarly charged particles moving side by side have two actions on one another, the one being an electrostatic repulsion, the other being an electro-magnetic attraction. When they have the 'ratio velocity' (see Chapter XVIII. § 5), or about the velocity of light, it is supposed that these two actions balance one another; when a smaller velocity, the electrostatic repulsion predominates; when a greater velocity, the electro-magnetic attraction predominates. But from the extreme difficulty there is in conducting such experiments with any certain data as to velocities, &c., there is still much that is uncertain and demanding further investigation.

CHAPTER XXIII.

DYNAMO-ELECTRIC MACHINES.

In the brief sketch of 'Dynamos' here given, the author has been guided mainly by the writings of Prof. S. P. Thompson. To these writings the student is referred for fuller information on this subject.

To the same authority the author is indebted also for the principle of the diagram given in Chapter XXIV. § 7; and to the courtesy of the publishers, Messrs. Spon & Co., for the use of the diagrams given in §§ 16, 18, 19, 21 of the present Chapter.

§ 1. General Nature of a Dynamo.'-We have seen in Chapter XXI. that when a conductor cuts lines of force in a magnetic field, there is an E.M.F. induced in this conductor; and that when a coil is moved in a magnetic field in such a way as to alter the number of lines of force piercing it, there is a resultant E.M.F. induced in this coil. At the end of § 4 in Chapter XXI. we indicated the manner in which this induced E.M.F. may be calculated.

Those machines on which we expend mechanical work in causing the necessary movements, and from which obtain electrical energy, are called dynamo-electric machines, or more briefly dynamos.

§ 2. General Account of Induced Currents. Let the symbols e, N1, N2, m, and have the same meaning as in Chapter XXI. § 4, end. Then we have in general

If the resistance of each turn of wire be R, then the resistance of the whole coil is m R. Hence, if the external resistance be r we have by Ohm's law an induced current C measured by

We have then a case similar to that of a series of voltaic cells arranged in series. By the principles of Chapter XIII. §§ 6 and 13, we can determine whether it is more advantageous to arrange the turns of wire in 'series,' or to arrange them 'parallel' so as to be equivalent to one turn of thicker wire, or to arrange them partly in 'series' and partly 'parallel.' It all depends upon the relative magnitude of R and r.

As an example we may consider the simple case of Chapter XXII. § 4. Let the area of the coil, measured in sq. cms., be S; let the number of turns of wire be m; let the strength of the earth's field be I; and let the coil be completely rotated a times per second. When the coil has its plane perpendicular to the lines of force, there are m IS marked lines of force piercing the circuit; this is because there are m turns of wire, and because the 'number of lines of force' piercing each sq. cm. measure the field-strength, as is explained in Chapter X. §§ 13 and 14, and in Chapter XVII. § I. When the coil is edgeways to the lines, no lines pierce it. When it has turned through 180°, so as to be again perpendicular to the lines of force, then mIS lines pierce it in the opposite direction. Hence there is a total change of 2 m IS lines. When it is turned through the remaining 180°, the same change occurs. For one complete revolution there is therefore a change of 4 m IS lines. And in one second there will be a change of 4a mIS lines. Hence, if by means of a commutator the contrary E. M.F.s induced in the two halves of a revolution be caused to give a current in a constant direction (see Chapter XXII. § 4, and § 4 of the present Chapter), we have

e = 4 am IS and C 4 am IS mR+ r

=

The reader is recommended to return to the general remarks of this and the last section when he has read the accounts of several dynamos described in what follows.

We may add that though large E.M.F.s may be obtained by means of dynamos, we cannot approach in magnitude the E.M.F.s obtainable by means of induction coils.

§ 3. Clark's Machine.-The simplest form of dynamo is that constructed on the pattern of the 'Clark's machine.' This has a field given by permanent magnets, and is therefore often called a magneto machine.

In Clark's machine there is a permanent magnet A that gives the field; the strength of this field can be regulated by connect

ing the two poles of the magnet completely, partially, or not at all, by a soft iron keeper. In 'medical coils' this regulator is an essential addition. In the front of the magnet poles there rotate two coils B and B' wound with one continuous wire in such a way that the E.M.F.s induced in the two

coils act in one direction along the wire. These coils are provided with soft iron cores in order to increase by magnetic

induction the number of marked lines of force piercing the coils. Let B and B' start from the position shown. Then, as we turn them through 180°, we first withdraw the lines that pierce them, and then introduce lines in the opposite direction. Hence the E.M.F. in each coil acts in one direction through this 180° of rotation; and the coils are so wound that the E. M.F.s of B and B' act in one direction. Through the second 180° of rotation the E. M.F.s are reversed; but a commutator, described in § 4, maintains the current in a constant direction in the external circuit.

The direction of current can easily be predicted from Lenz's law; for, as B leaves the N pole of the magnet and approaches

CC

the S pole, it will acquire on the side turned towards the magnet a S polarity, or the current will there run 'clock-wise,' since this will oppose the motion.

By giving a rapid motion and having many turns of wire we increase the a and the m of § 2, or increase the induced E.M.F. We can thus get an E.M.F. large enough to give shocks and small sparks.

§ 4. The Simple Commutator.-The figure here given represents a simple form of commutator. The one end of the wire is soldered to the metal piece o, and the other to o'; these pieces

pass each nearly half-way round the axis J, but are insulated from one another by two slits, one of which is seen in the figure. The axis itself is of ivory, ebonite, or some other insulating material. The circuit is completed by means of the metal springs b and c. Just as the coils are passing the position in which their E.M.F.s change direction, the metal springs b and c cross the two slits and come into contact each with that metal piece (o or o') that was just before in contact with the other spring. Thus the external current is maintained constant in direction.

The other metal piece, shown in the figure, is for another purpose that we need not describe.