160. The thumb rule; Ampère's swimming rule. The line-of-force diagram, fig. 59, shows further in which direction the deflection of the needle takes place. If we wish to have some simple rule connecting this direction with the direction of the current, we may conveniently make use of the disposition of certain parts of the body. For example, if we suppose the right hand to be laid upon the wire, so that the direction of the current is from the wrist towards the middle finger, the palm of the hand being turned towards the magnetic needle, then the north pole of the needle will be deflected in the direction of the thumb. In fig. 59, the hand must be held pointing from right (wrist) to left (middle finger), the back of the hand being turned downwards, since the wire passes beneath the needle.

Since the lines of force due to the current encircle the wire in the clockwise direction, while the north pole of a magnetic needle tends to move along them in the positive sense, the north pole must always be deflected in the direction indicated by the thumb; in the present case, towards the upper part of the figure. This rule we shall call the thumb rule;' it must be remembered that it refers to the right hand and the north pole of the needle. As regards the south pole, we have only to remember that its behaviour is exactly opposite to that of the north pole.

Another rule, due to AMPÈRE, is known by the name of the swimming rule. It supposes the whole body brought into the path of the current, and is stated as follows: Imagine yourself to be swimming in the conductor in the direction of the current, with your face turned towards the needle; then will the north pole be deflected towards the left and the south pole towards the right. In fig. 59, for example, the observer must be lying on his back, with his head to the left and his feet to the right, and looking up at the line-of-force diagram above him. The north pole of the magnetic needle will then be deflected towards his left, that is towards the upper part of the diagram, and the south pole in the contrary direction. In connection with AMPÈRE'S rule, we have to remember left hand = north pole.'

This swimming rule has come to be very extensively used; but we prefer the thumb rule, since the conception of the whole body in a position which may be highly uncomfortable is not so convenient as the employment of the hand alone. To apply Ampère's rule to a dynamo machine in motion might indeed be dangerous to life, for it is well known that in the effort to imagine the body in any particular position, we often attempt in some degree to practically realise our conception, and this might lead to an entanglement with driving belts, cranks and shafts.

161: Galvanoscope. The deflection which a magnetic needle suffers owing to a current flowing in a conductor parallel to its position of rest has been made the basis of a number of instruments which serve to detect the existence of a current. If a current is brought close to a magnetic needle which can turn freely in a horizontal or in a vertical plane, a deflection in one direction or the other will result, and will serve to show in which sense the current flows. The magnitude of the deflection will also furnish some idea of the number of lines of force arising from the action of the current, for it is immediately evident that the greater the number of these lines taking part in the phenomenon, the greater (cæteris paribus) the deflection of the needle will be.

162. Two magnetic poles in a plane perpendicular to the current. A magnetic needle must also be deflected when a vertical portion of a current-conductor, lying in the same magnetic meridian as the middle point of the needle, is brought near to either its north or its south pole.

Experiment 57.-Let a portion of a current-conductor, stretched straight and held in a vertical position, be brought from the north or from the south towards the corresponding pole of a declination needle, supported on a high stand, the direction of the current in the conductor being indicated by arrows. A deflection of the needle will take place, corresponding to the direction of the lines of force.

Here again the thumb rule, or Ampère's rule, may be applied. The line-of-force diagram for this case is shown in fig. 60.

In a longitudinal groove in the board C, near to the conductor (fig. 47), a little bar magnet is placed, its axis pointing directly towards that of the conductor; and in a plane just over the magnet the line-of-force diagram fig. 60 is formed.

Surrounding the cross-section S of the conductor is the concentric system of rings due to the lines of force of the

current (compare the diagram of the undisturbed field, fig. 48). At the side where the magnet is, with its source n and sink s, the two fields are superposed. The current in the present case is flowing upwards from below through the plane of the diagram, for the lines of force, as viewed from above, encircle the conductor counter-clockwise, as may be seen from their behaviour on encountering the poles n and s. If the little magnet is free to rotate about its middle point, it will accordingly be deflected (experiment 57). If the reader imagines his right hand to be thrust through the plane of the paper, the wrist being below and the fingers above (corresponding to the direction of the current), while the palm of the hand is turned towards the needle, then will the north pole be deflected in the direction in which the thumb points.

FIG. CO

163. Magnetic needle with one degree of freedom surrounded by a current loop. The effect of a current in deflecting a magnetic needle will be increased when the effects observed in experiments 56 and 57 are combined together. We may accordingly bend the current-conductor into the form of a nearly closed loop, surrounding the needle.

To obtain the line-of-force diagram in this case, we may make use of the following simple arrangement. Of two wooden

blocks, each about 12 cm. long, 8 cm. broad, and 2 cm. thick, one is used to support the upper part of the current loop. Through this block, perpendicularly to its face, two holes are bored about 5 cm. apart, and through the holes a n-shaped piece of thick copper wire is passed, the block being covered with a sheet of paper in which there are corresponding holes. The first block is laid upon the second, and in this there are small hollows filled with mercury into which the ends of the wire dip; the mercury being connected to terminals by means of metallic conductors. The line-of-force diagram can be easily prepared, and fixed on removing the loop. When the loop is about double as long as it is broad, the diagram obtained is very nearly the same as if the circuit around the needle were completely closed.

In the line-of-force diagram fig. 61, the points marked c, and c, are the places where the conducting wire passes. perpendicularly through

the plane of the paper. At c, the current passes from below upwards, while at c, it passes downwards again. Accordingly at c, the lines of force embrace the conductor counter-clock

FIG. 61

wise, and clockwise at c, where we are looking at the figure along the direction of the current. Between the points c,, Ca lies the needle ns, as is shown by the disturbance of the lines of force. Two bundles of lines of force due to the current, proceeding in opposite directions, are attached to the bar magnet. In the middle, at the indifferent zone, the two bundles meet. The tension along the lines of force tends to turn the needle out of the plane of the current loop which passes through c,, c, the north pole being urged towards the lower part of the diagram, the south pole towards the upper.

If the right hand be laid upon the conductor in the sense in which the current flows (i.e. with the wrist at c, and the middle finger pointing towards c), and if the palm of the hand be

turned towards the needle (i.e. downwards) the north pole n will be deflected in the direction of the thumb (i.e. towards the lower part of the diagram).

We shall see later that an arrangement similar to the above forms the basis of an important measuring instrument -the tangent galvanometer.

B.-Quantitative relations

That the field intensity at each point of an axial magnetic field may be determined in absolute measure, we must necessarily infer from Chapter IV., since the methods there given are of general application, and do not depend on the special properties of the field in question. It will be found, however, that for the field of force due to a current there is a single magnitude which serves to determine the whole field when the form of the conductor is given; in the case of a straight conductor, for example, we may calculate the field-intensity for every point when we know its value for a single point. The magnitude to which we refer is the so-called current strength.' In introducing this important conception we would lay especial stress on the fact that it can be defined with reference to magnetic quantities alone, so that we do not need to consider any phenomena of a kind different from those which specially concern us. The remainder of this chapter will accordingly be devoted to a description of various methods for measuring current strength,' and an investigation of the energy which resides in the field due to a current.

164. Fundamental electro-magnetic law. We have already learnt from an inspection of the line-of-force diagram in a plane perpendicular to a straight current-conductor (fig. 48) that the field-intensity in a coaxal magnetic system falls off as we pass to places more remote from the current. BIOT and SAVART made the first accurate investigation of the law according to which the decrease of intensity takes place, and they found that the field-intensity is inversely proportional to the distance from the conductor.

This