The C.G.S. unit thus obtained is, however, found to be far too great for practical purposes, and for these the 'farad' has been adopted as the practical unit of capacity. The farad is the capacity of a condenser in which a charge of one coulomb that is, the charge produced by an ampère of current flowing for one second-is required to produce between the plates of the condenser a difference of potential of I volt.

Since the quantity of electricity conveyed by an ampère in one second is 10-1 C.G.S. units and I volt=108 C.G.S. units, we have

Even this capacity, I farad, is very large, and it is found more convenient in practice to measure capacities in terms of the millionth part of a farad or a microfarad.

I

Thus I microfarad =

C.G.S. units.

1015

On the Form of Galvanometer suitable for the Comparison of Capacities.

The capacities of two condensers are compared most easily by comparing the quantities of electricity required to charge them to the same difference of potential, being directly proportional to these quantities.

Now the quantity of electricity required to charge a condenser to a given difference of potential will not depend on the resistance of the conductor through which the charge passes. The same total quantity will pass through the wire whatever be its resistance; the time required to charge the condenser will be greater if the resistance be greater, but, even if the resistance be many thousand ohms, the time of charging will be extremely small.

The effect produced on the galvanometer needle by a given quantity of electricity will be proportional to the num

ber of turns of the wire of the galvanometer; thus for the present purpose the galvanometer should have a very large number of turns. This, of course, increases its resistance; but, then, this increase does not produce any evil effect. A galvanometer of five or six thousand ohms may conveniently be used. The time of swing of the needle should. be considerable; a period of from two to three seconds will give fair results.

manner.

For the comparison of two capacities the damping does not matter greatly; it will affect all the throws in the same If, however, it be required to express the capacity of a given condenser in absolute measure, it will be necessary to use a galvanometer in which can be measured with accuracy. The time of swing, too, since it requires to be accurately measured, should be greater than that mentioned above.

81. Comparison of the Capacities of two Condensers.

(1) Approximate Method of Comparison.

Charge the two condensers alternately with the same battery through the same galvanometer, and observe the throws.

Let C1, C2 be the two capacities, B1, B2 the corresponding throws, the mean of several being taken in each case.

Then since the differences of potential to which the condensers are charged are the same for the two, we have (pp. 469, 471).

For making contact a Morse Key is convenient.

In this apparatus there are three binding screws D, E, F (fig. 78) attached to a plate of ebonite, or other good insulating material, above which is a brass lever. F is in connection with the fulcrum of the lever, E with a metal stud under one end, and D with a similar stud under the other. A spring keeps the front end of the lever in contact with the

stud connected to E, so that E and F are, for this position of the lever, in electrical communication.

A

On depressing the

other end of the lever this contact is broken, and the end depressed is brought into contact with the stud connected with D. Thus E is insulated, and D and F put into communication. In fig. 78, A and B are the

two poles of the condenser, G is the galvanometer, and c the battery. One pole, of the battery is connected with B, the other pole with D ; A is connected with the galvanometer G, and F with the other pole of the galvanometer, while B is also in connection with E. In the normal position of the key one pole of the battery, connected with D, is insulated and the two poles of the condenser B and a are in connection through E and F. Let the spot of light come to rest on the galvanometer scale, and observe its position. Depress the key, thus making contact between D and F, and observe the throw produced. The spot will swing back through the zero to nearly the same distance on the other side. As it returns towards the zero, and just before it passes it for the second time, moving in the direction of the first throw, release the key. This insulates D and discharges the condenser through the galvanometer, the electricity tends to produce a throw in the direction opposite to that in which the spot is moving, which checks the needle, reducing it nearly to rest. Wait a little until it comes to rest, and then repeat the observation. Let the mean of the throws thus found be d1.

Replace the first condenser by the second and make a second similar observation; let the mean of the throws measured as before along the scale be d2.

To eliminate the effect of alteration in the E.M.F. of the battery repeat the observations for the first condenser, and let the mean of the throws be 8,'. Now 8, and 8,' should, if

the battery has been fairly constant, differ extremely little; the mean (+81') should be taken for the throw.

Let D be the distance between the scale and the galvanometer mirror. Then, as we have seen (§ 71)

(2) 8

And if the ratio /D be small we may put for

sin tan n−1(¦¦)¦(see p. 45).

Hence we find from (1) and (2)

With most condensers a phenomenon known as electric absorption occurs. The electricity appears to be absorbed by the insulating medium, and continues to flow in for some time : it is therefore better, in this case, to put the galvanometer between E and B. By depressing the key for an instant the condenser is charged, but in such a way that only the discharge passes through the galvanometer; or, if preferred, the galvanometer can be put between c and D. and only the charge measured; or, finally, the wires conbeing preferably between B and D; when in the normal posinected to D and E may be interchanged, the galvanometer tion of the key, the condenser is charged, and a discharge, sudden or prolonged, is sent through the galvanometer on depressing the key. By these various arrangements the effects of alterations in the length of the time of charge or that there is no ready means of checking the swing of the discharge can be tested. They all have the disadvantage needle, and time is taken up in waiting for it to come to

rest.

This may be obviated by a judicious use of a magnet held in the hand of the observer, and reversed in time with the galvanometer needle, or still better by having near the galvanometer a coil of wire in connection with a second battery and a key. On making contact with the key at suitable times the current in the coil produces electro-magnetic effects, by means of which the needle may gradually be stopped. (2) Null Method of Comparing Capacities.

The method just given has the defects common to most methods which turn mainly on measuring a galvanometer deflexion.

The method which we now proceed to describe resembles closely the Wheatstone bridge method of measuring resistance.

Two condensers are substituted for two adjacent arms of the bridge; the galvanometer is put in the circuit which connects the condensers. Fig. 79 shews the arrangement of the apparatus. A, B1, A2 B2, are the two condensers; B1 B2

D on the Morse key, while E, the middle electrode of the key, is connected to B, and B. In the normal position of the key the plates of the condenser are connected through E and F. On depressing the key the contact between E and F is broken, and contact is made between D and F, and the condensers are thus charged.

is in connection with the axle of the key.