current in the conductor joining two of the points is independent of the E.M.F. in the conductor joining the other two, then those two conductors are said to be conjugate.

In the Wheatstone's bridge method of measuring resistances the battery and galvanometer circuits are made to be conjugate; the current through the galvanometer is independent of the E.M.F. of the battery. If the equation

P/Q R/S

hold, the galvanometer is not deflected whatever be the E.M.F. of the battery; there is no need, therefore, to use a constant battery. Moreover, since we only require to determine when no current flows through the galvanometer circuit, and not to measure a steady current, a sensitive

B

FIG. 66.

C

G

galvanoscope is all that is necessary; we do not need to know the relation between the current and the deflexion produced by it.

Fig. 66 is another diagram of the connections, which shews more clearly the conjugate relation. The conductors A B and C D A are conjugate if the equation P/Q = R/S holds.

It follows from this that we may interchange the galvanometer and battery without affecting the working of the method. The galvanometer may be placed between A and B, and the battery between C and D. The sensitiveness of the measurements will, however, depend on the relative positions of the two, and the following rule is given by Maxwell, Electricity and Magnetism,' vol. i. § 348, to determine which of the two arrangements to adopt. Of the two resistances, that of the battery and that of the galvanometer, connect the greater resistance, so as to join the two greater to the two less of the other four.

As we shall see directly, it will generally happen when

making the final measurements, that Q and s are greater than P and R; thus, referring to fig. 65, the connections are there arranged to suit the case in which the resistance of the battery is greater than that of the galvanometer.

To measure a Resistance with the Wheatstone-bridge Box.

Make the connections as shewn in fig. 65. Be sure that the binding screws are everywhere tight and that the copper wires are clean and bright at all points where there are contacts. This is especially necessary for the wires which connect R to the box. Any resistance due to them or their contacts will of course be added to the value of R. For delicate measurements contacts must be made by means of thick copper rods amalgamated with mercury, and dipping into mercury cups. The bottoms of the cups should be covered with discs of amalgamated copper, and the wires must press on to these with a steady pressure throughout the experiment; it is not sufficient to make the contact through the mercury by letting the wires drop into it without touching the copper bottom. The cups themselves are conveniently made of pill boxes, covered with a good thick coat of varnish.

See that all the plugs are in their places in the box, and press them firmly in with a screw motion to ensure efficient

contact.

Bring the control magnet of the galvanometer down near the coils, and if the resistance to be measured be not even approximately known, it generally saves time to shunt the galvanometer, using the shunt, provided there be one, if not, a piece of thin German-silver wire. Take two equal resistances out of the arms P and Q. Since it is probable that the galvanometer will be somewhat too sensitive even when shunted, it is better to take out the two 100 ohm plugs rather than the two 10 ohms. Then, since P = Q, R will be equal to s.

Take 1 ohm out from s. Make contact first with the

battery key K, and then with the galvanometer key K', and note the direction of the deflexion-suppose it be to the right.

Take out 1000 ohms from s, and note the deflexion— suppose it be to the left. The resistance is clearly between I and 1000 ohms.

Now take out 500 ohms-let the deflexion be to the left-R is less than 500. Proceed thus, and suppose that with 67 ohms the deflexion is to the left, and that with 66 ohms it is to the right. The resistance R is clearly between 66 and 67 ohms.

Now make P 10 ohms and Q 100, and at the same time remove the shunt, and raise the galvanometer magnet to increase the sensitiveness. Since Q is ten times P, s must be ten times R to obtain a balance. Thus s must be between 660 and 670. Suppose that it is found that with 665 ohms the deflexion is to the left, and with 664 it is to the right, the true value of s is between 664 and 665, and since R = PS/Q, the true value of R is between 66'4 and 66.5. We have thus found a third figure in the value

of R.

Now make Q 1000 ohms and P 10 ohms. Then, since Q is 100 times P, s must be 100 times R to secure the balance; and it will be found that when s is 6640 the deflexion is to the right; when it is 6650 it is to the left. The galvanometer may now be made as sensitive as possible; and it will probably be found that with a value of s, such as 6646, there is a small deflexion to the right, and with s equal to 6647 a small deflexion to the left. Thus the value of R is between 66.46 and 66'47.

If the fourth figure be required correctly, we may find it by interpolation as follows:

When s is 6646 let the deflexion to the right be a scale divisions, and when it is 6647 let it be b divisions to the left. Then since an addition of 1 ohm to the value of R alters the reading by a+b scale divisions, it will require an addition of a (at b) ohms to alter it by a divisions.

Thus the true value of R is 6646+a|(a+b) ohms, and the value of s is

66.46+a/100(a+b) ohms.

The exactness to which the determination can be carried will depend on the accuracy with which the small outstanding deflexions a and b can be read, and on the constancy of the battery.

If it be found that the resistance R is less than 1 ohm, make P 100 ohms, and Q 10; then the value of s will be ten times that of R, and if we find that s lies between 5 and 6, it follows that R is between 5 and 6; then make P 1000 ohms, and Q 10, and proceed similarly.

After making the determination the connecting wires must all be removed from the box and the plugs replaced. Experiment.-Determine the values of the resistances in the given box.

It has been shewn that if, in the Wheatstone's bridge arrangement, two of the conductors, as A B, CD (fig. 66, p. 548), are conjugate, then the current through the one due to an E.M.F. in the other is zero. It follows from this that the current through the other conductors is independent of the resistance in CD, and is the same whether CD be connected by a conductor or be insulated; for the condition. that the two should be conjugate is that C and D should be at the same potential, and if this condition be satisfied there will never be any tendency for a current to flow along CD;

the currents in the rest of the circuit will, therefore, not depend on CD.

FIG. 67.

с

Suppose, now, a galvanometer is placed in the branch DA, and a key in CD (fig. 67), there will be a deflexion produced in the galvanometer. Adjust the resistance s until the galvanometer deflexion is unaltered by making or breaking contact in the branch CD. When this is the case it follows that A B and CD are conjugate, and, therefore, that

S

RA

Р

R= X S.

Q

But R is the resistance of the galvanometer, which is thus measured by a null method without the use of a second gal

vanometer.

Fig. 68 shews the connections, using the Wheatstonebridge box. A considerable portion of the current from the battery flows through the

B

Q

K

D

FIG. 68.

S

R

K' galvanometer, and the needle is thereby deflected. If a Thomson's galvanometer be used in the ordinary manner, the spot of light will be quite off the scale. In order to ascertain if the adjustment of the resistances is correct the

mirror must be brought back to near its zero position by the aid of permanent magnets; it is probable that the control magnet will be too weak to do this alone, and others must be employed in addition. This constitutes one of the defects of the method; the field of magnetic force in which the needle hangs thus becomes very strong, and the sensitiveness of the galvanometer is thus diminished. By using a very weak electromotive force we may dispense with the