§ 5. Proof of Law II. by Torsion Balance.-Here we keep the same pole acting on the needle-pole n, but vary the distance. (See § 2, fig. i.) Now if we only keep the angle 0 small enough, the following statements will be approximately true.

(i.) When the needle is deflected through 0°, 10°, 10°, &c., the arm of the repulsive moment acting upon ʼn s remains constant, the force only changing.

(ii.) If the pole n be at a certain distance from the repelling pole when the deflexion is 0°, then at 10° it is at half this distance, at 0° it is at one-third of this distance, and so on.

The method is simple enough.

Let the needle be deflected through °, and let the torsion angle be (1 × 360 + a1)°. Then the total angle of torsion is (n1 × 360 + a1 + 0)°.

Now let us force the needle up to 40° by a larger angle of torsion (ng × 360 + a2)°. Then the total angle of torsion is (n2 × 360 + a2 + 10). (See §§ 1 and 2.)

Hence

=

Force at distance 0 n1 × 360 + a1 + 0
Force at distance 10 nɔ × 360 + a2 + 30°

If Law II. be true we shall find that this fraction comes out to

be 4.

So again for an angle of deflexion 40°, we should find that the ratio comes out to be; and so on.

We here suppose that the earth's action has been allowed for, or is relatively insignificant.

§ 6. Proof of Law II. by Method of Oscillation.-Using a 'short' needle we can count the oscillations at distances 10 cm., 20 cm., 30 cm., &c., from a given pole. The magnet whose pole we use should here-as in all cases where we wish to consider the action of one pole only-be so long that for all these distances the other pole has a negligible action on the vibrating needle.

Eliminating the earth's action as before, we get the ratio of the field-strengths at 10 cm., 20 cm., 30 cm., &c. If the law be true, then we should have

H10 H20 H30: &c. = 1 : 1

:: &c.

§ 7. Measurements as affected by Induction.-The same needle will give quite different results under the same external conditions if its own magnetism alters.

Hence, in all the above, where a needle is used for two or more measurements, and where it is assumed that there is no change in its magnetic moment, we must take care that the fields are not strong enough to alter its magnetism permanently.

This can be tested by vibrating it under the earth's action only before and after the series of experiments, counting the oscillations per second.

Even then there will be error due to the temporary alteration of the magnetic moment.

§ 8. Earth's Magnetism. General Ideas. We have spoken of the ‘earth's action,' implying that the earth acts as a magnet.

It does so act; but from the nature of the causes of its magnetic action we cannot give a simple account of the position of its poles or distribution of its magnetism.

The lines of force viewed as a whole (see Chapter II. § 11) would be seen to be wavy; and it would probably be seen that they converged to more than one north and south pole.

But it will give some idea if we say that the earth's action is nearly that which there would be if the whole earth were neutral, and if there were buried at the centre a powerful magnet about half as long as the earth's axis, whose position lay about 20° from the earth's axis, and varied from year to year and century to century.

This would give us lines of force lying horizontal over the equatorial regions, dipping more and more as we go north or south, and plunging perpendicularly into the earth at the points cut by the prolongation of the axis of our buried magnet.

Any magnetic needle used will be so very small with respect to the earth, that the lines of force will be with respect to it practically parallel, or the earth's field practically uniform. In fact, we could not detect any difference between the earth's field in different parts of the same room.

The earth's action therefore on a needle will be a pure couple, and will simply direct it.

If it were not so we ought to find besides the couple a horizontal force, or a vertical force, or both.

But experiment shows that no such force exists.

Experiments.—(i.) A needle floating on a cork shows absence of any horizontal force, by not moving in any direction.

(ii.) A needle weighed before and after magnetisation shows absence of a vertical force by absence of change in weight.

Note.-In what follows we shall often speak of the single force acting on one pole of a magnet needle, instead of the couple that acts on the needle as a whole. The reader will see that this is for convenience, and does not in any way contradict the above.

§ 9. Compasses.

Definition of magnetic axis.—A B represents a magnetic needle, perfectly symmetrical; its ends A B and its point of suspension O lying in a straight line.

If A B be also symmetrically magnetised, then it will come to rest with the geometric axis AO B lying along the lines of force acting upon it.

But if the needle be unsymmetrically magnetised, then, in the position of rest, some other line as n Os will lie along the lines of force. This line through O,

It ought to coincide with the geometric axis A OB; and in a wellmade lozenge-shaped needle this will be the case.

When an ordinary compass-needle comes to rest, the direction of its magnetic axis shows us the direction of the horizontal component of the earth's lines of force at the place where the compass is used. (For horizontal component, and resolution, see further on.)

This will be all that we can learn. Unless we have further information as to the declination (see § 11) at the place in question, we cannot tell the direction of the geographic north and south.

The mariner's compass differs from the ordinary compass in that the whole card turns on a pivot; there being several needles, parallel to each other, attached to the card underneath. There is a fixed mark on the side of the compass-box, and one reads off what point on the card lies against this mark; whereas in the other compass one reads off the point on the fixed card over which the needle has come to rest.

The compass-box is, moreover, provided with two sets of

pivots at right angles to each other, so that the card may remain horizontal in spite of the rolling of the ship.

§ 10. Modification of Earth's Lines of Force by the Presence of Iron Masses.—Any masses of iron or steel will modify the earth's field of force in their vicinity.

This disturbance of the fieid is of especial importance in ships, since there it may bear a large proportion to the whole field.

To render the magnetism of an iron ship as symmetrical as possible, it should lie along the lines of force while it is being subjected to the prolonged hammering during its construction.

§ 11. The Earth's Magnetic Elements.'-If we take any point on the earth's surface there will be through this point a line of force. This will lie more or less horizontally in equatorial regions and vertically in polar regions. In our latitude it will lie obliquely, dipping down towards the north. That vertical plane, through the point, that contains the line of force, is called the plane of the magnetic meridian; just as the vertical plane, that passes through the geographical north and south points, is called the plane of the geographical meridian.

The earth's field can be resolved into a vertical and a horizontal component in this plane, as we shall see further in § 13. It is the horizontal component that acts on the ordinary compass, so that the magnetic axis of the needle will come to rest in this line. Hence, the plane of the magnetic meridian can also be defined as that vertical plane that contains the magnetic axis of a compass-needle at the place in question.

At any place we know all about the earth's field when we know the three particulars given below. These are called the earth's three magnetic elements at the place.

(i.) The declination is the angle between the planes of the magnetic and geographic meridian. It is called west or east declination, as the needle points to the west or east of the geographic north respectively.

(ii.) The inclination is the angle between the direction of the lines of force and the horizontal plane. It is also called the dip.

(iii) The intensity is the field-strength measured in C.G.S. units, as explained in Chapter II. § 8.

Besides the 'elements' there are other terms that need explanation.

Variations are changes taking place (from hour to hour, day to day, year to year, and age to age) in any of the elements. Most of these changes, and probably all, are periodic.

Magnetic storms are 'irregular' disturbances, or those which as yet we cannot predict. The most powerful are those accompanying marked and sudden alterations in the sun, such as a sudden appearance or disappearance of sun-spots.

Magnetic equator is an irregular line round the earth's equatorial regions at all points along which there is no inclination, the lines of force being horizontal.

Iso-clinic lines answer to the parallels of latitude. They are irregular lines, only very roughly parallel to the magnetic equator, connecting points of equal inclinations.

Iso-gonic lines answer to meridians of longitude. They also are wavy and irregular. They converge towards points where the lines of force are vertical; points which would be called 'the earth's magnetic north and south poles,' only that there appear to be more than one of each, and each of these is perhaps not a point but an area.

§ 12. Measurement of Declination.-The finding of the angle between the planes of the magnetic and geographic meridian is effected by means of an instrument called a declinometer; this being provided with means by which we can find both meridians.

Near the base of the instrument is a compass-box with a very carefully graduated card, over the centre of which is suspended a compass-needle. This compass-needle is of lozenge shape, and has at each end a fine cross scratched. It is suspended in a sort of stirrup, so that it can be turned over if required. Thus, we can use it with either surface uppermost.

On a vertical axis, coinciding with the axis of suspension of the needle, and passing through the centre of the graduated card, turns a telescope. This telescope is provided with an objectglass so made that both distant and near objects can be viewed without altering the focus of the instrument. It is capable of being inclined to the horizontal plane as well as of turning about a vertical axis,

There is a fixed horizontal graduated circle and an index movable with the telescope, to tell us through what angle we turn the telescope about its vertical axis.