If A denote the density of dry air and W that of vapour at

saturation, the density of saturated air is A

W, or more

exactly A-608 W.

131

CHAPTER X.

MAGNETISM.

153. THE unit magnetic pole, or the pole of unit strength, is that which repels an equal pole at unit distance with unit force. In the C.G.S. system it is the pole which repels an equal pole, at the distance of 1 centimetre, with a force of 1 dyne.

If P denote the strength of a pole, it will repel an equal

P2

pole at the distance L with the force Hence we have

the dimensional equations

L2

P2L-2 = force = MLT-2, P2 = ML3T-2, P = M3L3T-1; that is, the dimensions of a pole (or the dimensions of strength of pole) are M3L3⁄4T ́1.

154. The work required to move a pole P from one point to another is the product of P by the difference of the magnetic potentials of the two points. Hence the

dimensions of magnetic potential are

work

MLT-2. M-L-T-MLT

Р

155. The intensity of a magnetic field is the force which a unit pole will experience when placed in it. Denoting

this intensity by I, the force on a pole P will be IP. Hence

IP = force = MLT-2, I= MLT-2. MLTML-T1; that is, the dimensions of field-intensity are M3L ̃3T-1.

156. The moment of a magnet is the product of the strength of either of its poles by the distance between them. Its dimensions are therefore LP; that is, MLT

Or, more rigorously, the moment of a magnet is a quantity which, when multiplied by the intensity of a uniform field, gives the couple which the magnet experiences when held with its axis perpendicular to the lines of force in this field. It is therefore the quotient of a couple ML2T-2 by a field-intensity ML-T-1; that is, it is MLT as before.

-1

1

157. If different portions be cut from a uniformly magnetized substance, their moments will be simply as their volumes. Hence the intensity of magnetization of a uniformly magnetized body is defined as the quotient of its moment by its volume. But we have

moment - MLT-1, L-3 = M3L ̄1T-1.

volume

=

Hence intensity of magnetization has the same dimensions as intensity of field. When a magnetic substance (whether paramagnetic or diamagnetic) is placed in a magnetic field, it is magnetized by induction, and the ratio of the intensity of the magnetization thus produced to the intensity of the field is called the "coefficient of magnetic

For

induction," or "coefficient of induced magnetization," or the " "magnetic susceptibility" of the substance. paramagnetic substances (such as iron, nickel, and cobalt) this coefficient is positive; for diamagnetic substances (such as bismuth), it is negative; that is to say, the induced polarity is reversed, end for end, as compared with that of a paramagnetic substance placed in the same field.

158. It has generally been stated that "magnetic susceptibilty" is nearly independent of the intensity of the field so long as this intensity is much less than is required for saturation. But R. Shida found ("Proc. Roy. Soc.," Nov., 1882), in the softest iron wire, a very rapid variation of susceptibility at low intensities. Under the influence of the earth's vertical force at Glasgow, 545, the susceptibility had the very large value 734 when the wire was stretched by a weight, and 335 when the weight was off.

Under a magnetizing force 2:35, the susceptibilities, with and without the weight, were 235 and 154.

Saturation was obtained with a magnetizing force of 80.7, which produced magnetizations 1390 and 1430, the susceptibilities being therefore 17.1 and 17.6.

With pianoforte wire (steel), the susceptibilities were 67.5 and 69.3 under the earth's vertical force, and 13.2 when saturation was just attained, with a magnetizing force of 107.5. The magnetization at saturation was 1420, being about the same as for soft iron wire.

With a square bar of soft iron nearly 1 centim. square, the susceptibility diminished from 19, under a magnetizing force of 18.2, to 7·6, under a magnetizing force of 189, which just produced saturation.

Examples.

1. To find the multiplier for reducing magnetic intensities from the foot-grain-second system to the C.G.S. system.

The dimensions of the unit of intensity are ML-T. In the present case we have M = 0648, L= 30·48, T=1, since a grain is 0648 gramme, and a foot is 30.48 centim.

grain-second unit of intensity is denoted by the number 04611 in the C.G.S. system. This number is accordingly the required multiplier.

2. To find the multiplier for reducing intensities from the millimetre-milligramme-second system to the C.G.S. system, we have

3. Gauss states (Taylor's "Scientific Memoirs," vol. ii. p. 225) that the magnetic moment of a steel bar-magnet, of one pound weight, was found by him to be 100877000 millimetre-milligramme-second units. Find its moment in C.G.S. units.

Here the value of the unit moment employed is, in terms of C.G.S. units, MLT-1, where M is 10-3, L is 10-1, and T is 1; that is, its value is 10. 10-10Hence the moment of the bar is 100877 C.G.S. units.