(2) Replace the magnet in its clamp with the N. pole uppermost (say). Place E at one end, and reduce the needle to complete rest.

(3) Give the needle a motion of rotation of about 20° by bringing an outside magnet or piece of iron near one end. Now remove this and all other magnets to a distance, and count the number of transits, N of one end in say two minutes, t, and repeat this two or three times, and take the mean as being more

accurate.

(4) Repeat (2) and (3) for about sixteen or twenty positions of the clamp on the magnet right up to the other end, and differing by about equal amounts, carefully noting where the needle turns round.

(5) Remove the clamp E and needle to a position quite free from the influence of everything except the earth's field, and note the number of transits in the same time, and tabulate your results as follows:

(6) Plot a curve having values of (”,2 ± ‚2) as ordinates (with due regard to their sign, which must be reckoned +, say when E is above the equator of the magnet, and ve when below), and distances along the magnet as abscissæ.

Inferences.-What sources of error is the method liable to, and from your curve state where the poles of the magnet are?

4. Distribution of Magnetism in Bar Magnets (Induction Ballistic Method).

Introduction.-Coulomb's vibration method of finding the distribution of magnetism in a bar magnet by the rapidity of oscillation of a small magnetic needle placed close to and at different parts of the magnet, is not an accurate one, owing (a) to

the close proximity of needle to magnet altering the distribution; (b) to inductive action of latter on the needle temporarily altering its strength, thereby making strong and weak fields relatively stronger and weaker respectively than they really are. The following method, depending on Faraday's principle of induction, was originally used by Rees, but is commonly called Rowland's method.

Apparatus.-Low-resistance ballistic mirror galvanometer, G; earth inductor, E (p. 359); magneto-inductor, I (p. 334), consisting of a bobbin wound with a large number of turns of insulated wire of low resistance, and capable of being moved rapidly through a fixed distance along the bar magnet, M, in a frame which may be clamped in different positions on M. If G, E, and I are in simple series, then on suddenly turning E through 180° so as to cut either the vertical or horizontal component of the earth's field, F1, the whole quantity of electricity in the transient current set up 2N, A,F,

Q

=

where N1

R1

= K sin 10°, causing a first throw d, scale-divisions,

=

= number of turns on E. A, their mean area in square cms.; R1 = total circuit resistance; K = "ballistic constant;" and 0,° angular throw in degrees. If I is now suddenly slipped along, it will cut a field, F, consisting of the lines of force which emerge from the surface of the magnet at the part over which I passes. Hence

=

= K sin 102, where N.R0° have the same meaning

Observations. (1) Connect up as mentioned, using the long flexible twin lead to connect G and E to I, which must be placed vertically some distance off. Adjust the spot of light to

zero.

(2) Make sure, by trial, at the start that the first throw (d) on G, produced by letting I slip in its frame by its own weight, is just on the scale; alter the controlling magnet of G to get this if necessary.

(3) Clamp the frame of I close up to one end of M, and observe twice over for this position the first throw on G when I falls. Note the mean (d) and the position (L) of I from one end.

In each case the spot of light must be absolutely at rest prior to

slipping.

(4) Repeat (3) about every 4 or 5 cms. along M, and tabulate as follows:

(5) Plot a curve with values of L as abscissæ and F, as ordinates.

(6) Find the position of the poles and distance between them by projecting the centre of gravity of each area on to the abscissæ.

5. Measurement of Magnetic Dip
(Dip Circle Method).

Introduction. The magnetic dip at any place is the angle which the magnetic axis of a magnetized needle makes with a horizontal plane when it is free to turn about a horizontal axis perpendicular to the magnetic meridian.

A magnet freed from all forces except magnetic ones would in the earth's magnetic field tend to point in the direction of a line of force at the place. This line of force, and consequently the magnet, will only be horizontal at or near the earth's equator. Hence, at any place for instance, in the British Isles-the magnet will "dip" considerably.

Errors to be avoided. (a) Error from eccentricity, i.e. axis of rotation of needle may not coincide with centre of vertical circle - eliminated by reading both ends of the needle; (b) magnetic axis may not coincide with axis of figure—eliminated by reversing the position of the axis of rotation of the needle. This is accomplished by rotating the box of the dip circle through 180°; (c) C.G. may not coincide with axis of rotation needle— eliminated by reversing the magnetic polarity of the needle;

(d) rolling friction-counteracted or minimized by gently tapping the base of the instrument. It is usually very small.

We will now consider these errors more in detail as follows:

Error (a).—In Fig. 5, I., the true dip is AOn or BON, and if there is eccentricity, what we read off at one end is AOn', and at the other BON'; but, since

I.

NNI

m

IV.

m

II.

III.

magnetic axis. Now, it is mm which sets itself in the "line of dip," whereas it is aB which is observed. Therefore, in IV. we get too large a value for the dip. If, however, we rotate the instrument in azimuth through 180° about a vertical axis, we shall be looking at the other face, and the dip will now be too small, as seen by V. Hence, the mean of the two gives the position of the magnetic axis mm, which is what we require.

Error (c).-In Fig. 5, II. and III., aB is the needle, G its centre of gravity, and O the axis of rotation. Hence, in II. it will

be obvious we shall get too large an angle of dip. If, however, the polarity of the needle is reversed so that the end B now dips, as shown in III., instead of a as before, the centre of gravity will now be above O, and hence the dip will be too small. The mean consequently gives the dip corrected for error (c).

H

F

FIG. 6.

If a magnetic needle is pivoted on a horizontal axis passing through its centre O, and is free to rotate in a

vertical plane parallel to the magnetic meridian of the earth, then, if F = the total force, and H and V the horizontal and vertical components of this force due to the earth

Observations. -(1) Carefully level the instrument, if necessary, by means of the levelling screws and spirit level. Lower the needle on to the knife edges if it is resting on the forked clamps.

(2) Turn the instrument in azimuth until, on gently tapping it, the needle lies vertically, pointing to 90° on the scale. Note the reading on the horizontal scale.

(3) Now turn it in azimuth through 90° from this position in (2), when the needle will then be swinging in the magnetic meridian.

(4) Read both ends of the needle to o'8° to avoid error (a). (5) Turn the instrument in azimuth through 180° and repeat (4) to avoid error (b).

(6) Reverse the polarity of the needle to correct for error (c), by means of a solenoid and current, and repeat (1)–(5).

N.B.-Before commencing the observations it is as well to first strongly re-magnetize the needle, in order to ensure maximum sensibility, and in all cases great care is required in removing it from the instrument for this purpose, in order to avoid bending or otherwise damaging the axis or pivots.

(7) Tabulate all your results as follows:

Therefore angle of "inclination" or "dip" at

1 For accurate work most elaborate forms of "dip circles" can be used, for a description of which the reader may refer to Gordon's "Treatise on Electricity and Magnetism," vol. i. The one used in this experiment is that shown on p. 335 of this book.