bismuth, the same magnetizing force would induce in the bismuth fewer magnetic lines than in a vacuum. But those lines which were induced

'would still run in the same general direction as in the vacuum; not in the opposite direction, as Weber and Tyndall maintained. The result of there being a less induction through diamagnetic sub

Fig. 188.

tances can be shown to be that such substances will be urged from places where the magnetic force is strong

to places where it is weaker. This is why a ball of bismuth moves away from a magnet, and why a little bar of bismuth between the conical poles of the electromagnet (Fig. 182) turns equatorially so as to put its ends into the regions that are magnetically weaker. There is no reason to doubt that in a magnetic field of uniform strength a bar of bismuth would point along the lines of induction.

Fig. 184.

373. Magne-Crystallic Action. In 1822 Poisson predicted that a body possessing crystalline structure would, if magnetic at all, have different magnetic powers in different directions. In 1847 Plücker discovered that a piece of tourmaline, which is itself feebly paramagnetic, behaved as a diamagnetic body when so hung that the axis of the crystal was horizontal. Faraday, repeating the experiment with a crystal of bismuth, found that it tended to point with its axis of crystallization along the lines of the field axially. The magnetic force acting thus upon crystals by virtue of their possessing a certain structure he named magne-crystallic force. Plücker endeavoured to connect the magne-crystallic behaviour of crystals with their optical behaviour, giving the following

law there will be either repulsion or attraction of the optic axis (or, in the case of bi-axial crystals, of both optic axes) by the poles of a magnet; and if the crystal is a "negative" one (i.e. optically negative, having an extraordinary index of refraction less than its ordinary index) there will be repulsion, if a "positive" one there will be attraction. Tyndall has endeavoured to show that this law is insufficient in not taking into account the paramagnetic or diamagnetic powers of the substance as a whole. He finds that the magne-crystallic axis of bodies is in general an axis of greatest density, and that if the mass itself be paramagnetic this axis will point axially; if diamagnetic, equatorially. In bodies which, like slate and many crystals, possess cleavage, the planes of cleavage are usually at right angles to the magne-crystallic axis. Another way of stating the facts is to say that in nonisotropic bodies the induced magnetic lines do not necessarily run in the same direction as the lines of the impressed magnetic field.

374. Diamagnetism of Flames. In 1847 Bancalari discovered that flames are repelled from the axial line joining the poles of an electromagnet. Faraday showed that all kinds of flames, as well as ascending streams of hot air and of smoke, are acted on by the magnet, and tend to move from places where the magnetic forces are strong to those where they are weaker. Gases (except oxygen and ozone), and hot gases especially, are feebly diamagnetic. But the active repulsion and turning aside of flames may possibly be in part due to an electromagnetic action like that which the magnet exercises on the convexion-current of the voltaic arc (Art. 448) and on other convexion-currents. The electric properties of flame are mentioned in Arts. 8 and 314.

LESSON XXX. - The Magnetic Circuit

375. Magnetic Circuits. It is now generally recognized that there is a magnetic circuit law similar to the law of Ohm for electric circuits. Ritchie, Sturgeon, Joule, and Faraday dimly recognized it. But the law was first put into shape in 1873 by Rowland, who calculated the flow of magnetic lines through a bar by dividing the magnetizing force of the helix "by the "resistance to lines of force" of the iron. In 1882 Bosanquet introduced the term magnetomotive-force, and showed how to calculate the reluctances of the separate parts of the magnetic circuit, and, by adding them, to obtain the total

66

reluctance.*

The law of the magnetic circuit may be stated as follows:

376. Reluctance. As the electric resistance of a prismatic conductor can be calculated from its length, cross-section, and conductivity, so the magnetic reluctance of a bar of iron can be calculated from its length, crosssection, and permeability. The principal difference between the two cases lies in the circumstance that whilst in the electric case the conductivity is the same for small and large currents, in the magnetic case the permeability is not constant, but is less for large magnetic fluxes than for small ones.

Let the length of the bar bel centims., its section A sq. cms., and its permeability μ. Then its reluctance

*This useful term, far preferable to “magnetic resistance," was introduced by Oliver Heaviside. The term reluctivity is sometimes used for the specific reluctance; it is the reciprocal of permeability.

will be proportional directly to 1, and inversely to A and μ. Calling the reluctance Z we have

2=1/Αμ.

Example. An iron bar 100 cm. long and 4 sq. cms. in cross-section is magnetized to such a degree that μ = 320: then Z will be 0.078.

The reluctance of a magnetic circuit is generally made up of a number of reluctances in series. We will first take the case of a closed magnetic circuit (Fig. 185) made up of a curved iron core of length 1, section A,, and

0

Fig. 185.

permeability ; and an armature of

length 2, section A, and permeability μ

in contact with the ends of the former. In this case the reluctance is

377. Calculation of Exciting Power..

Passing on to the more difficult case of a circuit made up partly of iron and partly of air, we will suppose the armature to be moved to a distance, so that there are two air-gaps in the circuit, each gap of length 1, (from iron to iron), and section A, (equal to area of pole face). This will introduce an additional reluc-. tance 21/A, the permeability for air being 1. It will also have the effect of making part of the magnetic flux leak out of the circuit.

=

By Art. 341, if the exciting power consists of C amperes circulating in S spirals around the core, the magnetomotive-force will be 47CS/10. Applying

Fig. 186.

this to the preceding example, dividing the magnetomotive-force by the reluctance, we get for the magnetic flux

But more often the calculation is wanted the other way round, to find how many ampere-turns of excitation will be needed to produce a given flux through a magnetic circuit of given size. Two difficulties arise here. The permeability will depend on the degree of saturation. Also the leakage introduces an error. To meet the first difficulty approximate values of μ must be found. Suppose, for example, it was intended to produce a flux of 1,000,000 lines through an iron bar having a section of 80 sq. centims., then B will be 12,500, and reference to the table in Art. 364 shows that if the bar is of wrought iron μ will be about 1247. To meet the second difficulty we must estimate (from experience) an allowance for leakage. Suppose we find that of all the lines created in the U-shaped part only the fraction 1/v gets through the armature, then to force N lines through the armature we must generate vN lines in the U-shaped piece, where v is the coefficient of allowance for leakage, an improper fraction increasing with the width of the gaps.

We then proceed to calculate in parts as follows:

Ampere-turns needed to drive N lines

through iron of armature.

Ampere-turns needed to drive N lines } = N x

through two gaps.

} = N

÷ 1.257.

Formulæ similar to this have been used by Hopkinson and by Kapp in designing electromagnets for dynamos. 378. Effect of Air-Gap in Circuit. - Air having no