from the preceding turn. Thus within the solenoid the magnetic force is very strong, while outside there are hardly any lines of force. The more nearly we approach the axis of the solenoid, the more exact is the parallelism between the lines of force; the field is uniform. Fig. 73 further illustrates the cross-pressure which the lines of force exert upon one another. The outer lines of the system bulge out into the spaces between the turns of wire, like elastic threads tied up tightly into a bundle, while just under the wire they are closely crowded together. Such a solenoid has far greater field-energy than its separate windings. At its ends, the lines of force diverge in all directions.

179. Equivalence of solenoids and bar magnets.--At one end of a solenoid lines of force emerge as they do from the north pole of a permanent magnet, while at the other end. they re-enter the solenoid, as would be the case at the south pole. Thus a solenoid, so far as concerns the external disposition of its lines of force, behaves exactly like a bar magnet.

If we follow out the direction of the current, we have at once a sufficient datum for determining from which end of the solenoid the lines of force emerge, which end, that is, corresponds to the north pole of a magnet, as well as the end where the lines re-enter, that is, the magnetic south end. Since the current-conductor embraces the lines of force in the clockwise sense, these lines will be passing into the interior of the solenoid at that end which, viewed from the outside, corresponds to a clockwise circulation of the current. On the other hand, that end which corresponds to a counter-clockwise circulation must appear as a source of lines of force, that is, as a north magnetic pole.

Model of the solenoid with its lines of force.-A helix, 30 cm. long and 5 cm. in diameter, is wound from thick copper wire overwound with red cotton or silk, the direction of the current in the wire being indicated by means of red arrows. Through the helix are threaded a number of model tubes of force (fig. 39), which are bent round into the form of closed curves (§ 127), their arrangement being such that the rotatory motions corresponding to the magnetic forces follow the same direction as the current.

These model solenoids are to be preferred to the usual cylinder with arrows marked upon it.

So far as concerns the external disposition of lines of force, our model will correspond exactly to that of the tubular magnet in fig. 42.

We may here notice how the model, with its interior rotational motions, may be used to explain the phenomenon of the electro-magnetic rotation of the plane of polarisation of light. If we suppose the periodically alternating circumstances which constitute a beam of light to be propagated along the lines of force through the interior of the solenoid, the variations of conditions, which take place transversely to the lines of force, will always be communicated to particles which are themselves in rotation about the direction of the lines of force as axis. We might be led to expect, then, that an alternation of conditions originally taking place in some determinate direction (a so-called plane-polarised beam of light), on being propagated along the axis of a helical current, would be somewhat rotated in the direction of the latter. This consideration formed the basis of Lord KELVIN's and MAXWELL'S conclusion that rotational motions exist in a magnetic field.

The following experiments show that a solenoid does actually behave like a magnet.

Experiment 58.--A long open wire helix, with arrows indicating the direction of the current and the corresponding direction of the lines of force within (most conveniently the model just described), is connected to terminals by means of conducting wires, so that it is traversed by a current. It is then brought near to the poles of a declination needle. All the deflection experiments described in § 38, corresponding to both the principal positions, may now be performed with the solenoid, just as they were previously performed. with the bar magnet.

Experiment 59.-To the ends of a solenoid made of thick aluminium wire, gold threads are attached by which it is hung up. When a permanent magnet is brought near to the solenoid on one side or the other, corresponding deflec

tions take place, and when the magnet is axially approached to the solenoid, phenomena of attraction and repulsion are observed, like those described in § 33.

Experiments may also be performed with AMPERE'S suspension (§ 151), the solenoid being provided with points which dip into mercury cups, but this method is not so convenient as that of the aluminium wire helix suspended by gold threads.

Although there is so close a resemblance between solenoids and magnets of the same external form, there is yet a very essential difference between them; this arises from the different spacial relations (cyclosis) existing in the fields of magnets and of currents. In the case of steel magnets, we cannot directly follow the course of the lines of force in the interior, we only suppose the lines are taken up and transmitted by chains of molecular magnets.

In the case of the solenoid, the course of the lines of force may be followed without hindrance throughout the whole interior, the medium being the same as in the surrounding space, and having the same permeability; we may pass along the lines of force right through the helix. from one side to the other, without encountering surfaces which separate media having entirely different magnetic properties.

180. Bobbins.-The effects produced by a solenoid are greatly increased when a greater number of lines of force are made to thread through its interior, that is, when greater and greater lengths of wire are wound upon the helix. When the length of the helix is increased the end effects' become less important, that is to say, the irregularity of distribution of the lines of force always existing at the ends, which behave in regard to the external field as sources of lines of force (compare fig. 73).

Solenoids of this kind, closely wound with several layers of insulated wire, we shall refer to as bobbins.

They must necessarily give rise to the same phenomena as the solenoids already examined, only in a greater degree, corresponding to the increased number of the lines of force.

Thus a bobbin is also characterised by the emanation and divergence of lines of force from one end (N), and their convergence to the other end (S), where they re-enter the helix.

Fig. 74 shows a view from above of an arrangement suitable for producing the fields with which we shall now be concerned. AA is a base-board, 16 cm. x 40 cm., standing on feet and provided with a wooden rim. From it project two supports BB, 18 cm. apart, each having a circular hole, 2.5 cm. in diameter, bored

through its upper half at the same height above AA. Through these holes is fitted a pasteboard tube C, of the same (external) diameter, and with walls about 2 mm. thick. In the figure, C is indicated by dotted lines. Insulated copper wire 1 mm. thick is wound upon it. The apparatus used for producing figs. 75-78 had five layers of windings, each consisting of 100 turns of wire, so that the total number of turns was 500, and the number of turns per unit length of the helix was 28. The ends of the wire are brought to FF.

To enable the observer to investigate the disposition of the lines of force inside and outside the helix, and especially at the ends, the lower half of the pasteboard tube is filled by a semicylinder of wood; wooden shelves DD are also fixed to the supports BB, at such a height that their upper surfaces lie flush with that of the wooden semi-cylinder. At the same height again there are wooden shelves running alongside the bobbin and terminating where they meet DD. Upon the horizontal table thus constructed is laid a sheet of paper, which has notches of the appropriate form cut in it, so that it may project far into the interior of the bobbin, and at the same time may fit closely round the outer boundary of the windings.

It is especially important to render directly evident the behaviour of permanent magnets and of pieces of soft iron in the field of a solenoid. To allow this, a groove EE is cut in the shelves DD and the inner wooden semi-cylinder, so as to run right through the helix from side to side. In this groove squareprismatic bar magnets or bars of soft iron may be laid.

We proceed to con

181. Magnetic effects of bobbins. sider a number of experiments with helices traversed by currents, showing the disposition of the lines of force in arrangements which have important applications, especially in technology.

Field of the pole of a bobbin.-We shall first consider the undisturbed divergence of lines of force from the end of a

FIG. 75

bobbin (fig. 75). The crosssections of the windings appear as two black patches in the lower part of the figure. The turns of wire, it must be remembered, do not extend right to the ends of these cross-sections, since the thickness of the support B intervenes (fig. 74). Within the bobbin the field is uniform, but where the lines of force appear, to the left of the diagram, they are already beginning to diverge. After the black rectangular patches which represent the section of the helix, there are no more windings, and here accordingly the lines of force diverge regularly and without hindrance into the external field. It will be noticed how the strong stream of lines of force through the interior of the bobbin spreads out on all sides as it passes through the open end. In the field facing the bobbin we shall place first of all bodies which are themselves sources of lines of force, and in the next place such bodies as have a far higher permeability than the surrounding medium.

(a) Action of a bobbin upon a permanent magnet.-In the channel E of the apparatus, fig. 74, is laid a power