the larger. On the larger bobbin c c are wound two distinct coils of insulated wire, one consisting of twelve convolutions, and having its ends attached to two of the binding screws, 1, 2, the other of four convolutions, and having its ends attached to the other two binding screws, 3, 4. If the binding screw 2 at the end of the first coil be joined by a piece of wire, as shown in the figure, to the binding screw 3 attached to the beginning of the second, the current will go 12+4, or sixteen times round the bobbin; whereas if the wire connect the end of the first coil, 2, with the end of the second, 4, and the current enter and finally leave the bobbin by the two binding screws 1, 3, attached respectively to the beginnings of the two coils, then the current will go twelve times round the bobbin in one direction and four times in the other, or practically 12-4, or eight times round the bobbin. Now, experiment shows that if a current of constant strength be passed successively first four, then eight, then twelve, then sixteen times round the bobbin, and if this is kept in a fixed position during the experiment, the tangents of the corresponding deflections produced will be as four to eight, to twelve, to sixteen, that is, simply proportional to the number of times the current passes round the bobbin.

In this experiment the current, after passing from the battery through the coils c c, and the key K, is led through the current indicator G, and through a variable length of wire w w back again to the battery. The stretched wires are, for safety, placed in a grooved box, v v, attached to the board which carries the whole apparatus, and the length of wire included in the circuit can be increased or diminished by adjusting the screw clamp s, which is so arranged as to slide along the groove. In this manner

the strength of the current can be altered, and if the insertion in the circuit of a greater or less number of coils on the bobbin c c, or any other cause, tends to vary the magnitude of the current, the screw clamp s must

E

be moved until the deflection of the galvanoscope G returns to its original value, thus showing that the current has the same magnitude as at the commencement of the tests.

These experiments prove that the sensibility of a tangent galvanometer is proportional to the number of turns of wire used on its bobbin. We may next proceed to investigate the effect of the size of the bobbin by experiments made on the small coil cc. The diameter of this coil is only one half that of c c, and there are four convolutions of wire wound upon it. When experiments are made it is found that, if the two bobbins cc and c c are placed so as to be in the same plane, and so as to have their centres coincident with that of the suspended magnet, the tangent of the deflection produced by any current flowing round the smaller one is twice as great as the tangent of the deflection produced by the same current flowing four times round the larger bobbin; and also, if the same current pass four times round the smaller bobbin in one direction, and eight times round the larger in the opposite direction, that no deflection is produced whatever the current may be.

From this we learn that the tangent of the deflection produced by a current, that is, the sensibility of the instrument is directly proportional to the number of convolutions of wire, and inversely proportional to the diameter of the coil.

In order, therefore, to get a sensitive instrument we should use coils of small diameter, and wound with many turns of wire, and it might be imagined that a tangent galvanometer intended for the measurement of very weak currents should be made in this way. As a matter of fact, however, the coils of good tangent galvanometers are always large in diameter compared with the length of the suspended needle; and the number of turns of wire used in winding is always limited by the consideration that the depth and width

of the channel in which the wire is wound must not exceed a certain fraction of the diameter of the coil. These restrictions are only imposed in order to ensure the fulfilment of the tangent law, and need not be considered when there is no necessity for the tangent of the galvanometer deflection to be strictly proportional to the current.

An instrument which is to be used as a tangent galvanometer must, however, be so constructed that all the conditions mentioned in § 22, page 84, as necessary to ensure the fulfilment of the tangent law are complied with. Now when the needle in the box g g, Fig. 52, is deflected, its poles move away from the coil c c, and the force exerted by the current in this coil is less, after the needle has moved, than before. The tangent law will not hold good unless the change produced in this way is small enough to be neglected. In order to test this point, the apparatus shown in Fig. 52 is arranged so that each of the coils cc, cc, can be moved either in its own plane or perpendicular to its plane. To facilitate this two grooves, e e, are made in the base-board, and cylindrical pegs are placed through holes suitably made in the base B B of the coil c c and work in these grooves, so that the coil can be slid along either in or perpendicular to its own plane. The grooves are graduated, and the alteration produced by moving the coil a given distance from the needle can be noted for each of the bobbins cc and c c.

Experiments of this kind will show that as the bobbin is moved the deflection alters, and that the change produced for the same amount of motion is proportionately greater for the small bobbin cc than for the large one C C. For example, if the coil be moved parallel to itself, and so that its axis passes through the centre of the needle, it will be found that the tangent of the deflection of the needle for a given current is proportional to

where r is the mean radius of the coil and x the distance from the mean plane of the coil to the centre of the needle. Now it is clear from this formula that for a given change in x there will be a greater change in the value of this fraction the smaller r is.

It thus becomes apparent that any error due to want of proper centering of the needle of a tangent galvanometer, or to the actual movement of its poles when it is deflected, must prove far more serious when the bobbins are small than when they are large; and for this reason instruments in which the tangent law is to be accurately relied upon are invariably constructed with large bobbins.

Fig. 53.-Mapping out the Fields produced by the Same Current Flowing Round Different Coils.

The law and variation of the sensibility of a tangent galvanometer with the number of windings and the diameter of the coil can be ascertained, and the practical importance of using a large coil for a tangent galvanometer experimentally illustrated, by employing three coils similar to the one used in § 20, instead of the apparatus shown in Fig. 52. These three coils (Fig. 53) are joined up in series, so that the same current necessarily passes through each, the diameter of the large coil is double that of either of the smaller, and the number of windings on the large coil and on one of the smaller are equal, and double that on the other small coil. For example, the large coil may conveniently be 30 centimetres in