those of discharge in rarefied air (Arts. 320 and 322). Yet the presence of an aurora does not, at least in our latitudes, affect the electrical conditions of the lower regions of the atmosphere. On September 1, 1859, a severe magnetic storm occurred, and aurora were observed almost all over the globe; at the same time

a remarkable outburst of energy took place in the photosphere of the sun; but no simultaneous development of atmospheric electricity was recorded. Aurora appear in greater frequency in periods of about 11 years, which agrees pretty well with the cycles of maximum of magnetic storms (see Art. 159) and of sun-spots.

The spectroscope shows the auroral light to be due to gaseous matter, its spectrum consisting of a few bright lines not referable with certainty to any known terrestrial substance, but having a general resemblance to those seen in the spectrum of the electric discharge through rarefied dry air.

The most probable theory of the aurora is that originally due to Franklin; namely, that it is due to electric discharges in the upper air, in consequence of the differing electrical conditions between the cold air of the polar regions and the warmer streams of air and vapour raised from the level of the ocean in tropical regions by the heat of the sun.

According to Nordenskiold the terrestrial globe is perpetually surrounded at the poles with a ring or crown of light, single or double, to which he gives the name of the "aurora-glory." The outer edge of this ring he estimates to be at 120 miles above the earth's surface, and its diameter about 1250 miles. The centre of the auroraglory is not quite at the magnetic pole, being in lat. 81° N., long. 80° E. This aurora-glory usually appears as a pale arc of light across the sky, and is destitute of the radiating streaks shown in Fig. 169, except during magnetic and auroral storms.

An artificial aurora has been produced by Lemström, who erected on a mountain in Lapland a network of wires presenting many points to the sky. By insulating this apparatus and connecting it by a telegraph-wire with a galvanometer at the bottom of the mountain, he was able to observe actual currents of electricity when the auroral beam rose above the mountain.

337. Electromagnetics. That branch of the science of electricity which treats of the relation between electric currents and magnetism is termed Electromagnetics. In Arts. 128 to 140 the laws of magnetic forces were explained, and the definition of "unit pole" was given. It is, however, much more convenient, for the purpose of study, to express the interaction of magnetic and electromagnetic systems in terms not of "force" but of " "potential"; i.e. in terms of their power to do work. In Art. 263 the student was shown how the electric potential due to a quantity of electricity may be evaluated in terms of the work done in bringing up as a test charge a unit of + electricity from an infinite distance. Magnetic potential can be measured similarly by the ideal process of bringing up a unit magnetic pole (N-seeking) from an infinite distance, and ascertaining the amount of work done in the operation. Hence a large number of the points proved in Lesson XXI. concerning electric potential will also hold true for magnetic potential. The student may compare the following propositions with the corresponding ones in Articles 263 to 268:

(a) The magnetic potential at any point is the work that must be spent upon a unit magnetic (N-seeking)

pole in bringing it up to that point from an infinite distance.

(b) The magnetic potential at any point due to a system of magnetic poles is the sum of the separate magnetic potentials due to the separate poles.

The student must here remember that the potentials due to S-seeking poles will be of opposite sign to those due to N-seeking poles, and must be reckoned as negative. (c) The (magnetic) potential at any point due to a system of magnetic poles may be calculated (compare with Art. 263) by summing up the strengths of the separate poles divided each by its own distance from that point. Thus, if poles of strengths m', m', m'"', etc., be respectively at distances of r', r', r''', from a point P, then the following equa

tion gives the potential at P:

(d) The difference of (magnetic) potential between two points is the work to be done on or by a unit (N-seeking) pole in moving it from one point to the other. It follows that if m units of magnetism are moved through a difference of potential V, the work W done will be

W = mV.

(e) Magnetic force on unit pole is the rate of change of (magnetic) potential per unit of length: it is numerically equal to the intensity of the field. Since by Art. 141,

ƒ = mH,

and work is the product of a force into the length

But

whence

through which its point of application moves forward, it follows that

W = f = mHl.

W = mV;

and

V = Hl,

H = V/l.

Example. The difference of magnetic potential between two points 5 centims. apart along a magnetic field in which there are 6000 lines per sq. cm., is 30,000. Or, it would require 30,000 ergs of work to be expended to push a unit pole from one point to the other against the magnetic force.

(f) Equipotential surfaces are those (imaginary) surfaces surrounding a magnetic pole or system of poles, over which the (magnetic) potential has equal values. Thus, around a single isolated magnetic pole, the potential would be equal all round at equal distances; and the equipotential surfaces would be a system of concentric spheres at such distances apart that it would require the expenditure of one erg of work to move a unit pole up from a point on the surface of one sphere to any point on the next (see Fig. 146). Around any real magnet possessing two polar regions the equipotential surfaces would be much more complicated. Magnetic force, whether of attraction or repulsion, always acts across the equipotential surfaces in a direction normal to the surface; the magnetic lines of force are everywhere perpendicular to the equipotential surfaces.

Flux of Force. From a single magnetic pole (supposed to be a point far removed from all other poles) the lines of force diverge radially in all directions. The space around may be conceived as thus divided up into