But after the constant of the instrument has been experimentally determined, in the way just described, this degree scale may conveniently be replaced by one graduated in square roots with which the P.D. can be read off directly in international volts.

The electrometer then becomes a direct-reading "electrostatic voltmeter" of the zero type.

50. Ammeters used as Voltmeters.-If an ammeter with its scale graduated in volts instead of (or in addition to) its being graduated in amperes has a low resistance, it will be suitable for measuring any small P.D. that may exist between two points separated by a small resistance. For example, it may be used to measure the P.D. between two points close together in a thick copper electric-light main through which a current is flowing, or to measure the P.D. between the terminals of a galvanic cell of very low internal resistance. On the contrary, if the resistance of the instrument alone, or the resistance of the instrument and its auxiliary wire, w, combined (Fig. 86) be high, it may be used to test a larger P.D. between two points separated by a larger resistance; for example, the P.D. between the positive and negative electric-light main in a house.

Beginners sometimes feel mystified that the same instrument is sometimes employed to measure a current and at other times a P.D.; that in the former case, when it is called an ammeter, it may be "short-circuited" with impunity, but must not be disconnected, whereas when it is called a voltmeter it may be disconnected but on no account may it be short-circuited.

The difference arises not from any intrinsic dissimilarity between an ammeter and a current voltmeter, but from the different ways in which the two instruments are employed. An ammeter is put into the main circuit in series with the rest of the apparatus, as is the galvanometer & in Fig. 85, page 170, and the ammeter a in Fig. 89, page 185, whereas a voltmeter is placed as a

branch circuit in parallel with the part of the circuit, the P.D. between the terminals of which is to be measured; for example, the zero electrostatic voltmeter E in Fig. 85, and the voltmeter v in Fig. 89. If the voltmeter be of the current type, then both it and the ammeter simply measure a current directly, but the current that the instrument G in Fig. 85 and A in Fig. 89 measures is the current flowing through the main conductor, K in Fig. 85 and c in Fig. 89 respectively, whereas the current that the voltmeter measures is the current that the P.D. between the terminals K1, K2 of the main conductor K or the P.D. between the terminals of the main conductor c will send through a resistance which is quite external to the main circuit, viz. the resistance of the voltmeter itself.

If the resistance of an ammeter be but a small fraction of the resistance of the rest of the circuit in which it is placed, the only resuit of short-circuiting the ammeter by bridging its terminals with a short piece of thick wire is to electrically remove the instrument from the circuit, for the current remains unchanged in strength, and practically the whole of it now passes through the short circuit: whereas in short-circuiting a voltmeter we short-circuit all that part of the circuit with the terminals of which the voltmeter is connected, and thus cause a great, and possibly a dangerous, increase in the current in the remainder of the circuit. For example, the shortcircuiting of an ammeter which is used to measure the electric-light current passing through a house will simply cut this particular ammeter out of circuit, whereas short-circuiting the voltmeter, which is placed across the house mains for measuring the P.D. supplied to the house, would momentarily extinguish all the lamps in the neighbourhood and compel the electric currentgenerating-station to produce an enormous current. Almost instantaneously either the piece of wire used to make the short circuit would itself be burnt up, or one of the "fuses," the name given to the pieces of easily-fusible metal placed in the circuit to diminish the

damage caused by such accidents, would itself be volatilised by the excessive current.

On the other hand, disconnecting one or both of the voltmeter wires from the main circuit stops, of course, the current through the voltmeter itself, but produces practically no effect on the main current, whereas disconnecting the ammeter stops the main current altogether, unless the ammeter has been short-circuited before being disconnected.

51. Moving Coil Voltmeter.-The moving coil ammeter, described in § 38, page 144, lends itself extremely well for use as a portable voltmeter in consequence of its freedom from outside magnetic disturbance, its quickness of action, its capability of being used in any position, and its great sensibility, so that the resistance of the coil and of the auxiliary wire w combined can be very high. Indeed, in a Weston voltmeter, intended to measure a maximum P.D. of about 140 volts, the resistance of the moving coil is about 100 ohms, and that of the auxiliary stationary wire about 16,000 ohms, which is a resistance far higher than that of any other type of voltmeter of the same range and quickness of action. The instrument, however, can only be employed to measure small currents, which is a disadvantage when it is desired to use it directly as an ammeter, but this becomes an advantage when the instrument is used as a voltmeter, since the smaller the current taken by a voltmeter, other things being equal, the better the voltmeter.

52. Calibrating a Deflectional Voltmeter.-If the law of the instrument be unknown as well as the P.D. in volts that produces any particular deflection, we can. calibrate the instrument throughout the scale in volts in one or other of five distinct ways.*

1. Place the voltmeter v to be calibrated in parallel with a zero electrostatic voltmeter E and apply different P.Ds. between the common terminals of the two

*For methods in which a Clark's cell is employed see §§ 153 and 154, pages 507 to 513.

instruments. Measure each P.D. in international volts by means of the electrostatic voltmeter and observe the corresponding deflection on the deflectional voltmeter.

2. If the voltmeter to be calibrated has a very much longer, or a very much shorter, range than the voltmeter with which it is to be compared--for example, if the one reads from 0 to 500 international volts, while the other reads from 0 to 60 international volts-then we may proceed as follows:

Place two conductors A B, C D (Fig. 88) in series, and, by using the method described in § 47, page 177, deter

mine the resistance of the two conductors in series A D relatively to that of one of them A B. For example, let it be found that the resistance of A D is ten times that of A B. The actual resistance of the conductors need not be known, but we must make sure that the resistances of the voltmeters whose calibrations we desire to compare are large relatively to the resistances of A D and of A B.

Attach the terminals of the voltmeter of the shorter range to the points A and B respectively, and the terminals of the other voltmeter to the points A and D respectively. Send different currents of suitable, but not necessarily of known, values through the conductor A D. Observe the corresponding readings of the two voltmeters, and remember that the P.D. between the

points A and D is always ten times the corresponding P.D. between the points A and B.

3. Join the voltmeter v (Fig. 89) to be calibrated to the terminals of a conductor c whose resistance o is known in international ohms. Send different currents in succession through this conductor, and measure the currents with the ammeter A. Observe the deflections of the voltmeter which correspond with each of the currents A1, A2, A3, &c., amperes, and note that they are produced by P.Ds. of A10, A20, Ago, &c., international volts.

If the voltmeter v be an electrostatic one, so that no current whatever passes through it, the deflection of the

Resistance.

ammeter A will measure the true current passing through the conductor c. If, however, v be a voltmeter that takes a current, then it must not be forgotten that the current passing through the ammeter is the sum of the currents passing through the conductor c and through the voltmeter. The error introduced by assuming that the ammeter measures simply the current passing through c will be the smaller the less is the resistance of c compared with that of the voltmeter. It will be better, therefore, that c should have a comparatively small resistance, and that the necessary P.D. should be produced between its terminals by sending a strong current through it.

If, however, there be a risk that such a current will warm the conductor c and so change its resistance, then it is better to join up the apparatus as in Fig. 90.