Liquids were placed in glass vessels and suspended between the poles of the electromagnet. Almost all liquids are diamagnetic, except solutions of salts of the magnetic metals, some of which are feebly magnetic; but blood is diamagnetic though it contains iron. To examine gases bubbles are blown with them, and watched as to whether they were drawn into or pushed out of the field. Oxygen gas was found to be magnetic; ozone has been found to be still more strongly so. Dewar has found liquid oxygen sufficiently magnetic to rush in drops to the poles of a powerful magnet.

The diamagnetic properties of substances may be numerically expressed in terms of their permeability or their susceptibility (Arts. 363 and 365). For diamagnetic bodies the permeability is less than unity. For bismuth the value of μ is 0.999969. The repulsion of bismuth is immensely feebler than the attraction of iron. Plücker estimated the relative magnetic powers of equal weights of substances as follows:

371. Apparent Diamagnetism due to surrounding Medium. It is found that feebly magnetic bodies behave as if they were diamagnetic when suspended in a more highly magnetic fluid. A small glass tube filled with a weak solution of ferric chloride, when suspended in air between the poles of an electromagnet, points axially, or is paramagnetic; but if it be surrounded by a stronger (and therefore more magnetic) solution of the same substance, it points equatorially, and is apparently repelled like diamagnetic bodies. All that the equatorial pointing of a body proves then is, that it is less magnetic than the medium that fills the surrounding space.

A balloon, though it possesses mass and weight, rises through the air in obedience to the law of gravity, because the medium surrounding it is more attracted than it is. But it is found that diamagnetic repulsion takes place even in a vacuum: hence it would appear that the ether of space itself is more magnetic than the substances classed as diamagnetic.

372. Diamagnetic Polarity. At one time Faraday thought that diamagnetic repulsion could be explained on the supposition that there existed a diamagnetic polarity" the reverse of the ordinary magnetic polarity. According to this view, which, however, Faraday himself quite abandoned, a magnet, when its N pole is presented to the end of a bar of bismuth, induces in that end a N pole (the reverse of what it would induce in a bar of iron or other magnetic metal), and therefore repels it. Weber adopted this view, and Tyndall warmly advocated it, especially after discovering that the repelling diamagnetic force varies as the square of the magnetic power employed. It has even been suggested that when a diamagnetic bar lies equatorially across a field of force, its east and west poles possess different properties. The experiments named above suggest, however, an explanation less difficult to reconcile with the facts. It has been pointed out (Art. 363) that the degree to which magnetization goes on in a medium depends upon the magnetic permeability of that medium. Now, permeability expresses the number of magnetic lines induced in the medium for every line of magnetizing force applied. A certain magnetizing force applied to a space containing air or vacuum would induce a certain number of magnetic lines through it. If the space considered were occupied by a paramagnetic substance it would concentrate the magnetic lines into itself, as the sphere does in Fig. 183. But if the sphere were of a permeability less than 1, the magnetic lines would tend rather to pass through the air, as in Fig. 184. If the space considered were occupied by

bismuth, the same magnetizing force would induce in the bismuth fewer magnetic lines than in a vacuum.

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. 183.

But

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 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 be 7 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.