The following are the actual results obtained in the calibration of the slide-wire of a bridge performed in the Physical Laboratory of the University College of North Wales by the method just described.

The numbers in the right-hand column are taken from tables. The results are of course not correct to the number of decimals given.

It will be noticed that the second reading in any line of the first column is not reading in the next line. being difficult to balance by adjusting the contact on the auxiliary wire. Balance was therefore obtained after a step was taken along the auxiliary wire by moving the slider through a short distance on the wire which was being calibrated.

exactly the same as the first This was caused through its

The value of r found as described below, p. 220, was

*0452 ohm. From this the resistance of the part of the wire between two readings of the scale is found as shown in the table.

A modification of this method which works well in practice and avoids some difficulties has been made by Prof. T. Gray. The two wires W, W', are arranged parallel to one another as in Fig. 58, and are connected at the ends A, C and B, D by two equal small resistances of suitable amount g. The equality of these resistances can be tested with great ease and delicacy by connecting

the battery at A, B, and balancing with the galvanometer between a point on Wand another on W', then transferring the battery contacts to C, D and observing if the balance is disturbed. If it is not the resistances are equal. When the resistances have been adjusted to equality, the battery is brought into contact at A and D and balance is obtained by placing one galvanometer terminal close to B on W, and the other at ʼn on W'. The battery contacts are then transferred to B and C, and balance is obtained by shifting the terminal of the galvanometer on W to some point a while that on

w' is kept at b. The battery contact is then transferred to A, D, and balance obtained by moving the terminal on W' so that the points of contact are a, e, and

so on.

The readings on the graduated scales are taken for the successive points of contact, and divide each wire, as will be shown presently, into steps each of resistance g.

The contact of the battery at A, D or B, C can be made by means of two simple rockers K, K, working between mercury cups or ordinary metal contacts, or by means of any simple key. This renders unnecessary any mercury cup switchboard arrangement for transferring coils.

Thus the method has the great advantage that the contacts are all permanent except those of the battery and the sliders, no one of which of course introduces any

error.

Let contact be made by the battery at A and D, and balance be obtained with the galvanometer at points a and e on the wires W and W', then calling as before z, z' the resistances of the wires between A and a, C and e respectively, and w, w the resistances of the whole wires, we have, neglecting (which will not affect the result) constant resistances of connecting bars, &c.,

Let the battery now be transferred to B and C and balance be obtained at d and e. Denoting the resistance between A and d by 21, we again have

The

or the steps along Ware steps of equal resistance. same can of course be proved for W'.

To avoid thermoelectric effects in such processes, the mean of the two positions of balance for opposite currents should always be adopted as the true position.

The slide-wire bridge may be used for the accurate comparison of resistance coils with a standard, say for the adjustment of single ohms with a standard ohm. Fig. 53 (p. 208 above) shows the arrangement adopted. 1 and 1⁄4 are the resistances of the coils a, b to be compared, and are nearly equal. r1⁄2 and r1⁄2 are the resistances of the two coils c, d, and are each nearly equal to 1 or r The connections are made by mercury cups as already described. Balance is obtained with the contact-piece somewhere near the middle of the slide-wire. The coils 71, 74, are then interchanged and balance again obtained. By (7) above we have

where 1, 2 are the resistances of the wire from A to the point of contact in the two cases. If p be the resistance per unit of length for the whole wire, S1, SÅ the distances (reduced, if necessary, by calibration, as shown above, to distances along a wire of uniform resistance p per unit of length) measured along the wire from A, we have

Τι

· r1 = p(S1 — S2).

(13)

These results are evidently free from any uncertainty as to the resistance of the junctions of the slide-wire to the

copper bars at its ends, and from any error due to want of correspondence between the index mark on the slidingpiece and the point of contact.*

If a separate experiment be made with a coil of accurately known resistance 1, just a very little less than that of the whole wire, and a second conductor of resistance r so small that it may be neglected, the value of p may be obtained from the equation

If the coils compared are too unequal to allow balance to be made on the wire, a series of intermediary coils may be obtained, so as to give a gradual descent from one coil to the other.

The resistance of the wire between any two readings may also be determined by the following method, which is due to Mr. D. M. Lewis. The total resistance of the wire is approximately found by measuring it with an ordinary bridge consisting of a post-office set of coils or other available form of a resistance box. Two coils are then made, the resistance of each of which is less than unity by a quantity which is nearly equal to, but not greater than, the total resistance of the wire. These can be also made by means of an ordinary resistance box. Let R1, R2 be the as yet not accurately known resistances of these coils. Each is tested as follows in the slide wire bridge against a unit coil, a standard ohm for example. The unit coil is first placed in the position a of Fig. 53 and one of the two resistances, R1 say, is placed in the

*The resistance of a coil may be accurately adjusted to any required value by first making it slightly too great, and then joining it in multiple arc with a thin wire cut so as to give as nearly as possible the required correction. If the observed resistance be r4, and that required 1, the resistance of the correcting wire is r1r/(~4 — ri).