It has been already mentioned that the number of lines of force which thread through the interior of a helix depends on the number of turns of wire, and on the strength of the current, that is to say, on the number of ampère-turns' ($175). Within a long helix the fieldintensity is the same for all cross-sections which are sufficiently far from the ends, its value being immediately deducible from the number of ampère-turns per centimetre of length.

If is the length of the helix, and if there are n turns of wire in all, then n/l is the number of turns per unit of length. If, then, there is a current of i ampères flowing in the circuit, the number of ampère-turns per cm. length of the helix will be n/lxi. This must be proportional to the field-intensity at any point within the helix. From considerations similar to those adduced in § 165 we may see that the field-intensity H corresponding to a current of i ampères through n turns of wire in a helix l centimetres long is

H=4π

ni 710

(33)

In the bobbin, fig. 74, n/l was about 28, and the current employed in making the line-of-force figures had a strength of 20 ampères 2 deca-ampères (i.e. 2 absolute electro-magnetic units), though such a current could only be kept circulating through the coil for a very short time. Thus the field-intensity in the interior was about 700 units, so that a unit pole placed within the helix would experience a force of 700 dynes, which, roughly speaking, is equal to the weight of 7 grams. In other words, 700 lines of force pass through each square centimetre of the cross-section of the interior. In the earth's magnetic field we found that there was about one line of force to each 2 cm.2 of perpendicular surface, so that our field is approximately 1400 times as strong as the terrestrial magnetic field in Central Europe.

185. The electro-magnet. The magnetic permeability of soft iron is more than 1,000 times as great as that of air. If, therefore, the interior of a helix is filled with this material, there will be a great reduction of magnetic resistance,' so that corresponding to a given number of ampère-turns

per unit length (that is, to a given magneto-motive force) we shall have a far greater number of lines of induction threading through the helix. At either end of a strong helix provided with an iron core the number of lines of force entering or leaving must accordingly be very great. A helix thus provided with an iron core is called an electromagnet.

Experiment 62.-A bobbin has the ends of its wire joined to flexible current-conductors, and is brought near to some iron nails; several of these will be drawn into the interior of the bobbin or will be held in contact with the ends. If now

we introduce into the bobbin an iron core which exactly fills it, the magnetic effects will be enormously increased, though an ampère-meter placed in the circuit shows that the strength of the current is unaltered. If the circuit is now broken (at some distant point) the nails fall away from the iron core, the magnetic effects having ceased, except for a small amount of 'residual magnetism.'

Since the iron core only increases the permeability of one part of the field of the current, the polarity of the ends of the helix (§ 179) will remain unchanged:

The north pole of an electro-magnet is that which (viewed externally) is encompassed counter-clockwise by the current, the south pole being that which is encompassed clockwise.

If a complete iron ring is overwound with one or more layers of insulated wire, through which a current is made to circulate, we have thus an electro-magnetically excited toroid. Here again the magnetic force in the interior is related to the number of ampère-turns per unit of length in the manner given by equation (33), § 184. Owing to the small magnetic resistance' of the circuit, and the absence of all demagnetising end-effects (§ 96), a toroid of this kind may acquire a very high degree of magnetisation 3, the values of the flux of induction I being correspondingly great. Accordingly such endless helical forms and closed electromagnetic circuits are largely used in investigating the magnetic properties of different kinds of iron, etc.

S

186. Some applications of electro-magnets. The applications of electro-magnets are so numerous and varied that we can here attempt no more than a very slight account of them. In the first place, all the experiments with permanent magnets described in Chapters I. and II. may be repeated with electro-magnets with far more powerful effects. To this end the electro-magnets are to be joined to terminals' by means of flexible conductors, or supported by strong gold threads.

Iron bars, either straight or bent into a horse-shoe form, may be overwound with insulated wire, thus furnishing us with electro-magnets of the bar or horse-shoe type. The fields of these have the same properties as those of the corresponding forms of permanent magnets. To show the form of their fields the coarsest iron filings may be used; these stand out to a considerable distance from the electromagnet, and render evident peculiarities in the remoter parts of the lines of force, such as could not be recognised in the case of ordinary magnets.

The lifting power of electro-magnets is very great, especially of those of the horse-shoe form. The iron armature sometimes remains attached to these latter even after the current has ceased to flow, an effect which is due to residual magnetism.

This residual magnetism in the cores of electro-magnets plays an important part in the working of the dynamo, as we shall see later. The poles of a large electro-magnet, of which we shall repeatedly have to make use, are distinguished by coverings of red and blue paper respectively.

Experiment 63.-A little bar of bismuth is hung up by a silk fibre attached to its middle, so that its axis rests horizontally, and a bar of iron of the same dimensions is suspended in a precisely similar manner. If the bismuth

is brought between the poles of a powerful electro-magnet, it sets itself across the direction of the lines of force, in virtue of its diamagnetic properties (equatorial setting, § 105). A much weaker magnetic field will suffice to show

1

that the iron bar sets itself along the direction of the lines of force.

But the great applicability of electro-magnets depends not so much on their strength as on the rapidity and ease with which their magnetic properties can be made and destroyed, especially since these changes can be effected from a distant position. All that need be done is to make or break contact at any point of the galvanic circuit. This is sometimes effected by the electro-magnet itself, as in the case of automatic contact-breakers (WAGNER'S hammer), continuously excited tuning-forks, and electric bells. The armature attracted by the electro-magnet is of soft iron, and is fastened to a spring which presses against a platinum point on the side remote from the magnet. The current passes between the platinum point and the spring, and through the fixed support to which the further end of the spring is attached, after which it passes in a helical path around the iron of the electro-magnet. When the circuit of the current is closed, the electro-magnet sends forth lines of force which pass very largely through the armature. This is accordingly attracted towards the magnet so that it no longer makes contact with the platinum point: the circuit is broken, the electro-magnet loses its magnetism, and the armature springs back to its former position. But as soon as the spring presses on the platinum point, the circuit is once more completed; thus the cycle of operations commences afresh, and continues to repeat itself automatically without any need for external interference.

In telegraphy, the circuit of a current is closed by depressing a key at the one station; this causes lines of force to embrace the conducting telegraph wire, a large number of these lines being gathered together by the core of an electro-magnet which is set up at the other station, and whose coils are included in the circuit. The electro-magnet thus attracts an armature which is attached to a mechanism of one kind or another, so that either marks are made upon a strip of paper drawn through the instrument—a dash for a continued contact and a dot for a momentary contact

as in MORSE's writing telegraph, or else some definite symbol upon a type-wheel is brought into position and printed upon the paper, as in HUGHES's printing telegraph.

Electrical clocks depend upon the making and breaking of an electrical contact by the pendulum of a standard clock. A metallic point is attached to the lower end of the pendulum, and dips for a moment during each swing into a drop of mercury, thus closing a circuit which includes a series of electro-magnets. These accordingly become magnetised and, each attracting an armature, cause a wheel in a system of clockwork to turn through the space of one tooth. In this way a single clock at a central station may be made to indicate the time with certainty at a number of secondary stations.