coil, is acted upon by a weaker couple in the same direction as is the lower needle.

Thus we can, by making the pole-strengths μ and very nearly equal, cause the earth's restoring couple to become very small, without diminishing the deflecting couple; and so can cause the galvanometer to become very sensitive.

(ii.) Next let two needles be fixed and suspended as before, but let the vertical planes through them make some small angle with each other. In fig. ii. we give a projection of the two

needles as viewed from above. 22 Let them further be of equal strength, so that μμ'.

=

Then it is pretty clear that with respect to the earth they will whose axis is at O, standing at right angle ; its pole-strength being 2 μ,

This can be made as small as possible

by making as small as we please. It is to be observed that the needles will stand so that n''s" is in the magnetic meridian; or the general direction of the two needles themselves will be E and W. The action of the current is as before.

6

9. The Controlling Magnet' Method.-A needle balanced so as to move in a horizontal field is influenced by the horizontal component of the earth's field only, as we have said before. Now we may superimpose on this horizontal field another due to a magnet; and, if the lines of force of this field run parallel to those of the earth's, but in an opposite direction, we may weaken, to any desired extent, the resultant field in which the needle moves, by suitably adjusting the strength of the magnet's field. The most convenient arrangement is to have a magnet directly above the needle, capable of being slided up or down a metal stem so as to make the field about the needle weaker or stronger; and also capable of revolving in a horizontal plane about the stem, so that it may either stand in the magnetic meridian or may make any angle with the meridian.

.

For our present purpose our object is to leave the needle directed in the magnetic meridian by a very weak resultant field.

We thus should have the magnet's field a little weaker than the earth's, and opposite in direction.

The needle is acted upon by the current as before; and, as the restoring couple is very small owing to the weakness of the restoring field, the instrument may be very sensitive.

We may add that in the most sensitive instruments the methods of §§ 8 and 9 are combined.

§ 10. Sir W. Thomson's Mirror Galvanometer.-The transmission of signals by means of interruptions and reversals of currents will be described in a future Chapter. At present we will merely observe that galvanometers will indicate such reversals and interruptions, and so will serve as instruments to receive signals of this nature. We shall see in a later Chapter that when such signals are sent through long submarine cables, the currents are very small on account of the great resistance; and further, that interruptions and reversals lose their abrupt character and become mere fluctuations in the weak current transmitted.

To indicate such weak currents and such slight fluctuations, Sir W. Thomson invented a form of galvanometer without which signals by cable would hardly have been possible.

in his mirror galvanometer we may notice the following main points of interest.

(i.) As the instrument is usually intended to be used in circuits where the resistance is already very great, there are often many thousand turns of (necessarily) fine wire; this multiplies' the strength of the field due to the current without perceptibly diminishing this latter. For the total resistance will not relatively

be much increased.

(ii) The 'needle' is a very small bit of magnetised watchspring. Having little mass and inertia, its movements follow any fluctuations in the current almost instantaneously.

(iii.) A controlling magnet enables one to vary the sensitiveness of the instrument at will, as explained in § 9.

(iv.) The same controlling magnet enables one, if need be, to bring the needle to rest in any position; and, aided by the method of suspension inentioned below, to work the instrument even on

board ship. In such cases we over-compensate the earth's field and direct the needle by the magnet alone. The fibres supporting the needle are fixed at top and bottom, and so prevent it from swinging against the sides of the coil in which it works.

(v.) To the needle is attached a very light mirror. A beam from a lamp falls upon this, and the reflected ray gives as index a spot of light that moves over a graduated scale.

We thus (as in the case of the quadrant electrometer of Chapter X. § 33) can have an index as long as we please, possessing no mass or inertia.

The figure on the opposite page indicates the coil, lamp, beam and its reflection, scale, and controlling magnet placed above the coil. The needle and mirror are inside the coil and are not seen. An additional controlling magnet T is sometimes of service in bringing back the spot of light to the zero mark.

Notes.-(i.) The mirror may be concave or plane. In the latter case an auxiliary lens is used, in order to bring the reflected beam to a focus on the scale.

(ii.) Either in the reading of, or in the construction of, the scale, we must make allowance for the fact (proved by elementary optics) that if the needle and mirror be displaced through an angle 0°, the reflected beam is displaced through an angle 20°.

SII. The Differential Galvanometer.-In the differential galvanometer the needle is suspended symmetrically between two coils. These coils must fulfil the following requirements.

(i.) Their resistance must be exactly equal, so that equal E. M.F.s at the terminals give equal currents.

(ii.) Equal currents in the same direction must give equal but opposite fields about the needle; so that, when the same current in the same direction is passing through the two, the needle is unaffected.

An exact test that these conditions are fulfilled is to send the same current through two coils coupled end-on, so that the current passes in the same direction through each coil. The needle should not be affected. Usually a small portion of one coil is left moveable, allowing exact adjustment to be made when the instrument is used..

It is clear that by coupling the coils suitably this instrument

may be used as an ordinary galvanometer, the two coils giving fields acting on the needle in the same direction.

The differential galvanometer has several uses. (i.) One use is to compare resistances; the method is somewhat as follows. A current is divided into two branches, passing through the two coils respectively. Since the resistances of these are equal, the currents will also be equal and the needle will be unaffected. The unknown resistance is now introduced into one branch, thus causing an unequal distribution of the two currents. Then known resistances are introduced into the other branch until the needle returns again to zero. When this is the case the resistances must be equal. In this method we are independent of changes in the E. M.F. of the battery.

(ii.) Another, less simple, use of this instrument is given in Fleeming Jenkin's 'Electricity,' p. 242, to which book we refer the student for details as to this method.

We will only say here that by shunting one branch of the galvanometer we may either measure a small resistance to a small fraction of an ohm, or may measure a resistance which is a large multiple of the greatest resistance contained in the resistance box.

§ 12. The Ballistic Galvanometer.--As we have seen, a current can be measured by the couple that it exerts (if we may use the expression) on a needle in an instrument of known construction; this couple depending also in a known way on the angle that the needle makes with the plane of the coil.

Now quantity of electricity is given by (current) × (time). Hence we can, in the case of steady currents, measure the total quantity of electricity that has passed by means of the tangent galvanometer, by observing both current and time of duration.

meter.

But supposing that we wish, eg, to measure the quantity of electricity in a condenser by discharging it through a galvanoIn the ordinary case we have a current whose strength rises from zero to a maximum, and then falls again to zero. While it passes the needle is deflected, and part acts when the arm of the couple is the full length / of the needle, part when the arm is I cos 0 (see § 5), where rises from zero to a maximum and then decreases again. It is impossible, under these conditions, to calculate in any simple way the total quantity that has passed. In order to do this an instrument is devised analogous to the ballistic pendulum used in mechanics. In this latter instrument we can estimate what are usually called 'impulsive forces,' or 'impulses,'