Example 27.-If a wire has 235 B.A. units of resistance, what is its resistance in international ohms ?

Answer.-231-85 international ohms.

Example 28.-If a wire of uniform cross-section has a resistance of 54 B.A. units at a certain temperature, by how much per cent. must its length be reduced so that it may have a resistance of 50 international ohms at the same temperature?

Answer.-54 B. A. units equals 54 x 0.9866, or 53.276, international ohms, therefore the length must be reduced 3.276 by or by about 6.15 per cent., in order that the 53.276' wire may have a resistance of 50 international ohms.

Example 29.-What resistances in legal ohms are respectively equal to 100, 200, 300, 400, and 500 international ohms?

Answer.-100-235, 200-47, 300-705, 400-94, 501.175 legal ohms.

47. Current Method of Comparing P.Ds.-From Ohm's law it follows that the current flowing through any conductor at constant temperature is directly proportional to the P.D. between its terminals. Such a conductor may be a coil of a galvanometer, or it may consist of a galvanometer G together with a wire w (Fig. 86) in series with it. And no matter how the shape of

Differences.

the circuit composed of G and w may be altered, provided that the joint resistance of G and w together is not changed, the current passing through the galvanometer will be directly proportional to the P.D. which is main

tained between T1 and T2, the terminals of the arrangement. If then the galvanometer has been calibrated relatively for current, it is calibrated for the relative measurements of be set up P.D. which any between T1 and T2 by connecting their terminals with any conductors between which a P.D. exists.

may

In place then of employing the zero electrometer (Fig. 83) we may use the combination of galvanometer and auxiliary resistance w to compare, for example, the P.D. between the points A and B (Fig. 87) with the P.D. between the points C and D in the conductor ABCD conveying a steady current. For the P.D. in question will be simply proportional to the two currents that flow through the galvanometer when the terminals T1, T2

(Fig. 86) are connected respectively first with the points A and B and then with the points C and D.

Further, since the resistance of a conductor is the name given to the ratio of the P.D. between its ends to the current that flows through it, and, since the current that flows through AB is necessarily the same as that flowing through CD, it follows that

current when T, and T2 are joined to A and B

2

current when T1 and T, are joined to C and D

2

the current in each case being the current through the galvanometric arrangement (Fig. 86).

Consequently, if the value of one of the resistances A B or C D be known in international ohms, the value of the other in international ohms can be at once found by the method of testing just described.

48. Reason for Using High Resistance Galvanometers for P.D. Measurements.--When using a galvanometer for the comparison of two P.Ds., or for the comparison of two resistances by the method described in § 47, it is not necessary that the galvanometer should be calibrated absolutely in amperes, for, as we have just seen, all that is required to be known is the ratio of the currents that produce different deflections, not the actual value of these currents in amperes. But there is one condition in connection with the galvanometric arrangement Gw (Fig. 86) that it is most important to fulfil, and that is the condition that the application of the terminals T1, T2 to the points A and B or to the points. C and D does not alter the distribution of potential that previously existed in the conductor A B C D. In fact, the test must not alter the thing tested, an all-important rule to remember in experimenting.

Whenever a galvanometer, properly constructed and calibrated, is introduced into any circuit the galvanometer measures the current flowing after the gaivanometer has been inserted, but this is not necessarily the same as the current that flowed before the galvanometer was inserted. These two currents will only be the same in value when the resistance of the galvanometer is small compared with that of the rest of the circuit, and when the other conditions remain unchanged. It will, therefore, be only under these special circumstances that the deflection of a galvanometer will measure the current that passed through the circuit before the circuit was disturbed by the insertion of the galvanometer into it.

Similarly, whatever be the resistance, small or large, of a galvanometer or of a galvanometric arrangement Gw (Fig. 86), provided that this resistance remains quite

constant, the relative P.Ds. between two pairs of points A and B, C and D, can be accurately compared by means of this galvanometric arrangement, only it must be carefully remembered that the P.Ds. that are thus compared are the values existing after the joining of the terminals T1, T2 to the points A and B, or to the points c and D, and not the values of these P.Ds. before the application of the measuring instrument. And it will be only when the resistance of G and w combined is very large compared with the resistance of the conductor AB and also with the resistance of the conductor C D that the application of the galvanometer will produce no disturbance in the distribution of potential along the conductor

A B C D.

Therefore for P.D. measurement it is desirable that the galvanometer & and the auxiliary conductor w should together have a high resistance, and that the required sensibility of the galvanometer should be attained by winding the galvanometer with a large number of convolutions of fine wire.

49. Voltmeter.-A "voltmeter" is an instrument which enables the P.D. between its terminals to be read off directly in international volts. Whether the voltmeter be of the electrostatic type and its action depend on the attraction of electrified bodies, or whether it be of the galvanometer form and the P.D. be indirectly measured by the current it produces through a fixed resistance, it is obviously necessary that the sensibility of the instrument should not be affected by moving the instrument from place to place. In fact, a voltmeter must possess the constancy of an ammeter, with the addition that its resistance must be quite constant, and any ammeter of practically constant resistance when graduated to indicate the P.D. between its terminals in international volts, instead of the current passing through it in amperes, becomes a voltmeter.

The electrometer described and illustrated in § 42, page 164, gives the same reading for the same P.D.

between its terminals if the instrument be levelled each time after being moved. Its relative calibration is, of course, known since our fundamental definition of the relative value of P.Ds. is based on the use of this electrometer. If then we ascertain the P.D. in international volts (say V1) that must be set up between the terminals T1, T2 of the instrument so as to bring the pointer p to the zero position when the index c has been turned through some particular angle, say a1, the P.D. in international volts V2 corresponding with any other angle a through which the index c must be turned to bring p to zero is known from the equation

2

A P.D. whose value is known in international volts can be applied to the terminals T1, T2 of the electrometer V1 (and so the constant can be experimentally found) a1

by connecting T and T, to the ends of a conductor, c (Fig. 89, page 185), whose resistance in international ohms, o, has been ascertained, and through which flows a current of A amperes, as measured by the ammeter a. For this P.D. is equal to A x o international volts.

This constant is about 2:37 for the zero electrometer illustrated in Fig. 83, page 164, that is to say, the index c has to be turned through about 360° to bring the pointer p to zero when a P.D. of 45 volts is maintained between the terminals of this instrument.

The dial at the top of the electrometer is initially graduated into degrees or other divisions of equal value.