Calibration of Ballistic Galvanometer by Means of a Standard Cell and Condenser.

239. If a condenser having a capacity of K farads is charged to a potential of V volts, the quantity of electricity stored in it in coulombs is

Q = KV

Since the capacity of standard condensers is usually measured in microfarads, it will have to be divided by 106 to bring it to farads before using in the above formula.

In order to calibrate the ballistic galvanometer by this method, it is connected up with a battery, condenser, and suitable key, so that the condenser may be charged or discharged through the galvanometer. The following diagram (Fig. 103) shows

placed in series with the ballistic galvanometer BG and the discharge key K; the other terminal of the galvanometer being connected to the upper contact (2) of K, to the lower contact (1) of K through the standard cell B, and to earth.

When K is depressed on contact (1), the condenser is charged, and the amplitude of the first swing of the needle noted. By raising K to the upper contact (2) the condenser is discharged. This should be repeated several times, and the mean of the swings taken; also, if necessary, with several cells in series. The E.M.F. of the cell is corrected for temperature, and the value of Q calculated as shown above. K may be measured by a method to be described in the next chapter, or if a standard condenser is used it will be known. The cell B and the key

K must be carefully insulated from earth. If the galvanometer

to be calibrated is one in which the sine of half the angle of swing of the needle is proportional to the quantity of electricity discharged through it, then—

where the capacity potential and swing of the needle have the values K1, V1, and a, respectively, and the constant of the galvanometer K will therefore be-

and the quantity of electricity corresponding to any throw of the needle will be-

The condenser method of calibration may also be employed in obtaining the absolute calibration curve of a D'Arsonval galvonometer for quantity of electricity. The condenser in this case being charged to different potential differences, either by employing several standard cells in series or by standardizing, by means of a Clark cell, the fall of potential down a long uniform wire, and charging the condenser across various known lengths of the wire. A curve may then be plotted with scalereadings for abscissæ and corresponding quantities of electricity in coulombs for ordinates, the distance of the mirror from the scale-division and relative value of the controlling force being specified.

240. In a calibration of a ballistic galvanometer by means of a standard condenser and known E.M.F., a battery of two Leclanche cells in series was connected to a resistance of 10,000 ohms; whilst a condenser of 10 microfarads capacity was charged through the ballistic galvanometer across 300 ohms of the 10,000-ohm resistance. A ballistic swing of 230 scaledivisions was obtained, the scale being 2000 scale-divisions distant from the mirror. The difference of potential across a coil of 1000 ohms resistance, which formed part of the

10,000-ohm resistance, was then carefully measured on a potentiometer against a standard Clark cell, and was found to be o'280 volt. The difference of potential employed to charge the condenser was therefore

The angular swing of the spot of light = 6'55° The angular swing of the galvanometer needle a = 3'27

Remarks on the Use of the Ballistic Galvanometer.

241. In using a ballistic galvanometer, where great accuracy is not required, and the swings of the needle are small, the sines of the angles of swing are nearly proportional to the angles themselves, and therefore, in a comparison of two quantities of electricity, the ratio of the amplitudes may be taken instead of the ratio of the sines of the half-angles.

The student will probably experience some difficulty at first in reading the exact value of the swing of the needle, this becoming more difficult the quicker the periodic time of swing of the needle. A few trial swings should be taken first, and thus the part of the scale reached by the spot of light will be located; the observer may then at once turn his attention to this spot after having completed the circuit. A sliding pointer moving over the scale may be used with advantage to locate the exact position of the swing. It is advisable, however, for measurements of this kind, that there should be at least two observers.

242. As stated before, the needle of the galvanometer must be perfectly stationary before the discharge is sent through the coils. To enable this to be attained quickly, a small auxiliary coil, connected to a battery through a reversing key, and known as a damping coil, may be set up near the galvanometer, so that when a current is flowing in it, its magnetic field will act on the galvanometer needle. By properly timing the duration and direction of the current in this coil, the needle may be rapidly brought to rest. It has been stated that almost any type of galvanometer may be used ballistically; for accurate work, however, a special design is necessary, since the damping in

most galvanometers is pretty large, and when this is so, the correction is difficult, and cannot be made by taking the logarithmic decrement, but the galvanometer must be calibrated directly in coulombs per degree of swing, throughout the scale, by some of the inductor methods which are independent of the damping. A special form of ballistic galvanometer, designed by Messrs. Nalder Bros., is shown in Fig. 104; in it the magnets, which are bell-shaped to diminish air-friction, are arranged astatically, two being at the centre of the coil and two outside, one above and one below the coil.

The coils, which are hinged to give easy access to the needle, are mounted in ebonite cases, and the whole highly insulated; there is as little solid metal as possible in the vicinity of the needles, as eddy currents might be set up, which would increase the damping action. The mirror is also reduced in size as much as possible, on account of air-friction.