varying the ratio of c to d. For example, the resistances c and d may be the resistances of different lengths of the same kind of wire, in which case we know that c will be to d simply as the ratio of these lengths, whatever be the absolute resistance in ohms of the two parts (see

§ 81, page 254). A form of Wheatstone's bridge, in which PTQ, of Fig. 123, was one piece of stretched wire, and the ratio of the "proportional arms" c to d varied by moving the connection of the wire leading to one terminal of the galvanometer, was originally employed by the Electrical Committee of the British Association, and is, for this reason, sometimes called the "British Association bridge"; at other times, the "metre bridge,"

from the stretched wire being often a metre long. The wire may be made of platinum, or better still, of platinumiridium, which, being very hard, tends to prevent the wire from being worn at any part.

To protect the platinum-iridium wire from being accidentally knocked or damaged, it may conveniently be placed in a groove cut in the edge of an ebonite or slate disc, D (Fig. 126), and contact made with any point of it by means of the spring key к carried at the end of the movable radial arm A, and shown in detail in Fig. 126a. The small pin under the knob K is to prevent the knob being pressed down so much as to damage the platinum-iridium wire. The circuit of the battery B (Fig. 126) is closed by a separate key к'.

The scale round the edge of the disc in Fig. 126 is divided into centimetres and millimetres, but for rapid work it is more convenient to have this scale divided into ratios, as indicated for a few points in the following, where the top line of numbers gives the length of the platinumiridium wire measured from the left hand, the second line of figures the ratio of the length on the left to the length on the right, and the third line the ratio of the length on the right to the length on the left :

∞

0 10 20 30 40

0

9

50

0.111 0.250 0.429 0.667 1
4

2.333 1.500 1 0.667 0.429 0.250 0.111 0

A form of metre bridge of greater range is shown in Fig. 127. It has three stretched wires ww, each a metre in length, and so arranged that either one of them alone, or two of them in series, or all three in series, can be made use of to form the two sides c and d of the Wheatstone's bridge (Fig. 123). When the plug E is, as in the figure, placed in the hole H, the current simply passes through the stretched wire which is nearest to the observer. If, on the other hand, the plug E be put in the hole h, then, since the brass plate P is permanently connected with the plate p by a thick copper strip under

in series with the one farthest from him. Lastly, if the plug, be removed altogether, the three wires are in series.

the base of the instrument, the middle stretched wire is short-circuited, and the wire nearest to the observer is

3

The object of thus lengthening the wire is to increase the sensibility of the test when desired, and a still further increase in the sensibility can be effected by removing the short-circuit pieces S1, S2, and inserting coils of known resistance in place of them. For example, suppose that the ratio of the unknown to the known resistance be then the slider K must be placed so as to divide the stretched wire into two parts having this ratio. Hence, if one of the three wires only be used, the lengths of the two parts which will give exact balance will be 60 and 40 centimetres, and an error of 1 centimetre in the position of the slider will correspond with an error in the determination in the ratio of

61 39

1.5

60
40

× 100 per cent., or 4.3 per cent.

If, on the other hand, the three wires in series be employed, then the lengths into which the three metres of wire must be divided to obtain exact balance will be 180 and 120 centimetres, and an error of one centimetre in the position of the slider will correspond with an error in the determination of the ratio of

181

119

1.5

180
120

× 100 per cent., or 1.4 per cent.

If now two coils, each having a resistance equal to, say, 500 centimetres of the stretched wire, be inserted in place of the short circuit pieces s, and s2, an error of a centimetre in the position of the slider will only corre spond with an error of

781

519

780

520

1.5

× 100 per cent., or 0.32 per cent.

Contact between the platinum-tipped knife-edge k and one or other of the stretched wires, is produced by

depressing the knob K, which causes the lever, L L, to which this knife-edge is attached to turn on an axis a a. On removing the pressure, the lever is pressed up by a spring underneath it; and the slider should never be moved with the knife-edge k depressed, as this would scrape the stretched wire and alter its diameter. In order to enable k to make contact with either the first, second, or third wire, the knob K is not fastened rigidly to the lever, but can slide along it in a slot, and be so placed that the near end of the spring s rests in either one of three grooves on the top of the lever, L L, corresponding with the three positions of k when it is in contact with the three stretched wires respectively.

77. Bridge Key.-In using a Wheatstone's bridge it is desirable to send the current through the four arms of the bridge a, b, c, d, before it is allowed to pass through the galvanometer, and this is especially important when testing the resistance of the copper conductor of a long submarine cable, since the current in such a case takes an appreciable time to reach its maximum value and become steady, due to the cable acting as a "condenser" (see Volume II.). Hence, if the galvanometer circuit were completed when the battery was attached to the bridge, an instantaneous swing of the galvanometer would be produced, even if a bore to b the ratio of c to d. And although, since the ratio of resistances having been effected, the deflection of the galvanometer would become nought as soon as the current in the four branches of the bridge became steady, great delay in the testing would be caused by this first swing of the needle. A similar difficulty would occur in measuring the resistance of an electromagnet or even of any coil without an iron core, if it were not specially wound; because whenever a coil is so wound that a current passing through it produces magnetic action, a short interval of time has to elapse, after putting on the battery, before the current reaches its maximum, or steady, value, arising from what is called the "self-induction" of the coil.