pole of the magnet be m P, its length 7 L, and the intensity of the field at the place iF per P; then the couple experienced is iml F by L arm.

The dependence of this couple, so far as it depends on the magnet itself, is expressed by the factor

ml P by L distance between poles.

This is the idea of magnetic moment.

Consider a bar

ART. 208. Intensity of Magnetization. magnet L long and of uniform cross-section a L2, which has been magnetized longitudinally, so that its poles are near its extremities. Suppose this bar divided longitudinally and cross-wise into small bars. The magnetic moment of such small bar is proportional to its length and to its cross-section. Hence we have the idea of intensity of magnetization, which is expressed in the form i P by L = L long by L2 cross-section.

In the case of the bar magnet considered, i is constant throughout both in direction (the direction of the axis of the moment) and in amount; hence the moment of the bar is

ila P by L.

When a magnet is not uniformly magnetized, the direction and magnitude of the intensity of magnetization vary from point to point; and in consequence one value of i can be considered constant only within a small region.

The

ART. 209. Declination, Dip, Horizontal Intensity. earth acts as a magnetic body in producing a field of magnetic force in its neighbourhood. The intensity at any point in the field is fully specified by stating its magnitude and the direction of the lines of force. It is, however, more convenient to measure the horizontal component of the intensity than the intensity itself. The direction of the line of force is specified by the declination, that is, the angle between the North and the direction of a magnetic needle free to move in a horizontal plane (Fig. 25); and by

the dip or inclination, that is, the angle between the former direction and the direction assumed by a magnetic needle free to move in that vertical plane (Fig. 26).

Let the horizontal component be hƑ horizontal per P, and the dip 8 degrees; then the total intensity is

h sec 8 F along per P.

MAGNETIC ELEMENTS OF TOWNS IN GREAT BRITAIN, FOR JAN., 1884.*

ART. 210.-Determination of the Horizontal Intensity. When a magnet performs small oscillations freely in a horizontal plane, under the influence of the magnetic field of the earth only, the following relation holds true

4 T2(M × L2) x (vibration/T)2= (F/P) x (P x L);

in which M by L2 is the unit for moment of inertia about the centre of figure (Art. 161), F per P the unit for the horizontal intensity, and P by L the unit for the magnetic moment of the magnet.

EXAMPLES.

Ex. 1. Two magnetic poles, 7 and 9 C.G.S. units respectively, are placed at a distance of 5 cm. apart; find the force in grammes between them.

Ex. 2. A magnetic needle, the magnetic moment of which remains constant, is suspended so as to move freely in a horizontal plane. When deflected from the magnetic meridian at three different places on the earth's surface, it is observed to oscillate 7.5, 8.3, 10-4 times respectively in one minute. Compare the intensities of the earth's horizontal magnetic force at the three places.

As the moment of inertia and the magnetic moment of the needle are constant, we have (Art. 161)

kƑ horizontal per P = (vibration per minute)2. Hence the three horizontal intensities are as

Ez. 3. The absolute horizontal intensity of the earth's magnetic force at London is 3-8 in terms of the foot-grain-second unit. Find its value in terms of the C.G.S. unit.

The intensity at a place is expressed in terms of F per P. Now 1F=M LTT, 1P2=MxLTTx L;

and

1. If the horizontal intensity of the earth's magnetic force at a place is 3·8, and the vertical 8.5, what is the total intensity?

2. When two long magnets of equal strength are placed in a straight line at a distance of 1 mm., the repulsive force is 3,290 dynes. Find the strength of a pole.

3. A small freely suspended magnet performs 72 oscillations per minute under the action of another magnet. How many would it perform if the distance between them were half as great again?

4. At various places on the earth's surface a declination needle vibrates 70, 60, and 50 times per minute. Compare the horizontal intensity at the three

places.

5. Find the number of foot-grain-second units of intensity of magnetic field equivalent to one C. G.S. unit.

6. The horizontal component of terrestrial magnetic force at Glasgow is about 16 C.G.S. unit. Find to two places its amount in terms of the foot-grain-second unit.

7. The dip at Paris in 1880 was 66°, and the total intensity 47 dynes per Pc.g.s. What was the horizontal intensity?

8. If the value of the magnetic moment of a magnet be 10, when the units of length, mass, and time are the centimetre, gramme, and second, what will be the value of the magnetic moment when the units are the metre, kilogramme, and minute?

9. The bearing of a ship's compass from a station on shore is N. 44° 20′ E., and the bearing of the station by the ship's compass, taken at the same time, is S. 50° 50′ W. What is the deviation for this position of the ship's head?

10. Find by means of Art. 161 the moment of inertia about its centre of figure of a bar magnet, which is 5 cm. long, and has a section of 2 mm. square.

11. The horizontal intensity of the earth's magnetic field at Göttingen was found by Gauss to be 1·782 millimetre-milligramme-second units. Express it in terms of the C.G.S. unit.

SECTION XLVII.-ELECTROSTATIC.

ART. 211.-General Unit of Electricity. Any unit of quantity of electricity may be denoted by Q.

There are two laws, by means of either of which the unit of electric quantity may be defined; namely, the electrostatic law, and the electromagnetic law. The electrostatic law states how the repulsive or attractive force between two quantities of electricity depends on the magnitude of each, and on the distance between them. The electromagnetic law states how the intensity of the magnetic field depends on the current in the influencing wire. A unit of quantity defined by the former law, as well as any derived unit, is called an electrostatic unit; while a unit of quantity, defined by the latter law, as well as any derived unit, is called an electromagnetic unit.

ART. 212. Electrostatic Unit of Quantity. The law of re