251. The Potentiometer. With an especially arranged resistance box, called a compensation apparatus or potentiometer, the method described above for comparing electromotive forces becomes very convenient, and is perhaps the most precise method known. The resistance box is constructed so that the resistance in one circuit remains constant while that in the branch circuit is varied through all possible values.

One of the most convenient forms of compensation apparatus has its parts arranged as shown in Fig. 159, its total resistance being 14999.9 ohms. The following order of adjustment may be followed. The standard cell, a Clark element for instance, is connected at S; the unknown electromotive force,

which may not exceed 1.5 volts, is connected at X; a galvanometer at G; and a battery in series with a resistance of 5000 ohms or more is connected as shown at B and P. This battery must have an electromotive force somewhat greater than 1.5 volts; it may be a single accumulator cell, or two gravity or Leclanché cells. The several switches are to be set to indicate the significant figures of the electromotive force of the standard cell. If the Clark cell is at the temperature 19°, for example, its electromotive force is 1.4279. Set the switch of the thousands row at 14, the hundreds switch at 2, the tens at 7, the units at 9, and the tenths switch at 0. Then the resistance of

that part of the main circuit to which the galvanometer is connected is 14279.0 ohms. Turn the switch D to 100000, which places a safety resistance of 100000 ohms in the circuit of the standard cell corresponding to Q of Fig. 158. Now adjust the resistance P so that upon closing the key K there will be no deflection of the galvanometer. Turn D to 10000 and improve the adjustment of P if required; and finally turn D to 0, which cuts out the safety resistance, and perfect the adjustment of P till no deflection results from closing the key.

This makes the instrument direct reading, in that the number of ohms required for compensation is exactly ten thousand times the electromotive force of the cell attached, the standard in this case.

Turn the switch D back to 100000, and turn the switch C to X, which places the unknown cell in the compensation circuit. By adjusting the resistance levers of the potentiometer, place them so that again there is no deflection when the key is closed; turn D to 10000, and improve the adjustment, and finally turn D to 0, and perfect it. The reading of the various dials of the potentiometer is then ten thousand times E, the electromotive force of the cell X being tested.

The potentiometer may be used without the extra resistance P, but it is then not direct reading, and the proportion of the previous article is to be used in computing the unknown electromotive force. In this case also the unknown electromotive force may have any value not exceeding that of the battery B.

CXLII. ELECTROMOTIVE FORCE WITH A CONDENSER Compare the electromotive forces of several cells with that of a standard cell by means of a condenser.

252. Comparison of Electromotive Forces with the Condenser. -If a condenser (Art. 262) is charged from several different sources, the charges received will be proportional to the electromotive forces of the sources. By measuring these charges the electromotive forces may be compared. This method has the

advantage that the cells are used only on open circuit, thus avoiding polarization.

Connect a ballistic galvanometer, G (Art. 253), a condenser, C, a charge and discharge key, K (Art. 263), and one of the cells to be tested, B, as indicated in Fig. 160. The key being in charge position, the condenser will receive a charge proportional to the electromotive force, E1,

of the cell. By pressing the key firmly, but for a very short time, upon the galvanometer contact, the condenser will discharge through the galvanometer, and will deflect

B

K↑

the needle through an angle, 91, FIG. 160. CONDENSEr Method such that sin 01 is proportional to

the charge. By substituting for the cell first used a second one of electromotive force E2, a deflection, 02, will be obtained. If the distance of the scale from the mirror is D and the two observed scale readings are d1 and do,

E1: E2 = sin 01: sin 0, sin tan-1

=

d

:sin tan-12.

D

D

If the angular deflections of the needle do not exceed 6°, the sines and tangents may be taken as proportional to the corresponding arcs, and then

E1: E2 = d1 : d2.

Any number of cells being thus compared, if one of them is a standard, the electromotive forces of the others may be determined.

(CAUTION.

Do not allow the cells to be short circuited nor to be directly connected to the galvanometer.)

253. The Ballistic Galvanometer. A ballistic galvanometer is one designed to measure the total quantity of electricity passing through it in a current of very short duration. The needle must have a period so long that the current will have ceased before it has moved appreciably from its position of rest. The needle should have the least possible damping. The quantity of

electricity thus passing through the galvanometer is proportional to the sine of half the angle of the first swing of the needle.

The deflections of the needle are usually measured by observing with a telescope a centimeter scale as seen reflected in a mirror attached to the needle. The following adjustments are essential. If the galvanometer is of the suspended magnet type

(Art. 209), the plane of the coils must be in the plane of the magnetic meridian ; and the suspension must be so adjusted that when the needle is at rest the torsion is zero, and so that the needle is magnetically symmetrical with respect to the plane of the magnetic meridian. If the galvanometer is of the suspended coil (D'Arsonval) type, the effect of the earth's field may be neglected; and it is sufficient that the torsion of the suspensions is zero when the needle is at rest, and that the plane of the coil is parallel to the force of the stationary field magnets. The direction of the mirror will usually indicate whether these conditions are approximately fulfilled, while a sufficient test of the accuracy of the adjustment is that equal charges sent through the galvanometer in opposite directions produce equal and opposite deflections. Fig. 161 represents a high sensibility D'Arsonval galvanometer, which is exceedingly convenient for ballistic observations.

FIG. 161

D'ARSONVAL GALVA

NOMETER

In addition to these adjustments of the galvanometer it is necessary that the telescope and scale be so placed that the mirror when at rest reflects to the cross wires of the telescope that point of the scale which is in the same vertical plane as the axis of the telescope.

When these adjustments are made the observed displacements of the scale, when the needle is deflected, are proportional to the

tangents of twice the angles of deflection. Tables are often provided, giving corrections, which, when added to the scale readings, make these readings directly proportional to the arcs, or to some function of the arcs, whose tangents they measure.

After a ballistic galvanometer has been deflected, some special manipulation is required to bring the needle quickly to rest. If it is of the suspended coil type, a short circuiting of the galvanometer is the most efficient method. The current induced by the motion of the needle in the field of the magnet reacts upon the needle, damping its vibrations. If the galvanometer is of the suspended magnet type, the motions of the needle may be checked by the manipulation of a permanent magnet held in the hand; or by temporarily connecting to the galvanometer a small coil of wire which is arranged to slide over the end of a fixed bar magnet. By moving this coil on the magnet an induced current is produced whose direction and strength are easily controlled, and which can be made to bring the needle to rest. When this is accomplished the circuit of the auxiliary coil is broken. If the needle cannot be brought entirely to rest, the condenser may be discharged precisely when the needle is at a turning point in its vibrations, and the deflection is to be calculated from this turning point and not from the point of equilibrium.

For further consideration of the ballistic galvanometer, see Arts. 267 and 268.

CXLIII. ELECTROMOTIVE FORCE WITH THE QUADRANT ELECTROMETER

Compare the electromotive forces of various cells.

254. The Quadrant Electrometer. The quadrant electrometer has four metallic quadrants, which together form a short cylindrical box, the quadrants being supported within a metal case by insulating posts and separated from one another by small spaces; the alternate quadrants are connected by wires, and each pair is connected to an insulated binding post outside the case; within the quadrants a flat aluminum needle is