Important advances in geomagnetism followed in the next two centuries [Chapman and Bartels, 1940, volume 2, chapter 26; Nelson et al. 1962]:

1. The discovery by Gellibrand in 1635 of the slow variation of the Earth's field [Malin and Bullard., 1981; Brush and Banerjee, 1988]. Graham [1724] (see Chapman and Bartels, [1940, section 26.9]) of "magnetic storms" (later term), large irregular disturbances of the compass needle.
2. The first magnetic survey of the Atlantic Ocean by Halley, in 1699 [Bullard, 1956; Ronan, 1969; Evans, 1988].
3. The discovery by Oersted in 1820 that electric currents produced magnetic forces [Shamos, 1959; Dibner, 1962].
4. The laws of electromagnetism, by Ampére in 1821 [Williams, 1965, 1989].
5. Electromagnetic induction, by Faraday in 1831 [Faraday, 1952; Williams, 1963, 1965].

    In 1839 Carl Friedrich Gauss [Gauss, 1839, 1877; Dunnington, 1955] published a method for mathematically describing the Earth's field B by means of a scalar potential γ

expanded at any point (r, θ, φ) in spherical harmonics:

    The first sum represents sources inside the Earth, and the second one external sources. Gauss and his associate Wilhelm Weber then went on to found a network of observatories, greatly expanded by British and Russian help [Cawood, 1979; Malin, 1969]. From data thus obtained, the coefficients due to sources inside the Earth were derived [see Barraclough, 1978]; as for the external coefficients, the calculation gradually confirmed what had been suspected, that better than 99% of the field originated inside the Earth. However, as Graham's work suggested, some magnetic effects did originate on the outside. Observations of such effects were advanced by the work of Charles Coulomb, who in 1777 greatly increased the sensitivity of magnetic measurements by suspending a magnetic needle from a fine string [Gillmor, 1971; Shamos, 1959]. Such instruments could be made even more sensitive by attaching a small mirror which moved a spot of light, and this type dominated geomagnetism for close to 200 years [Nelson et al. 1962; Multhauf and Good, 1987].

    Enter the Sun. In the first half of the nineteenth century there lived in the German town of Dessau a pharmacist named Samuel Heinrich Schwabe whose hobby was astronomy [Newton, 1958]. Every day when the Sun was not obscured, Schwabe observed it, paying attention to sunspots, noting their numbers, and keeping a tally of days when they were absent [Meadows 1970]. He started observing in 1826 and 10 years later published a report of his results: no one seemed to pay attention. In 1843 he published a more complete account, suggesting a l0-year cycle: at first, again, no response. Eventually, however, Schwabe's work caught the eye of Alexander von Humboldt, naturalist and promoter of the sciences, who in 1851 included Schwabe's results in his third volume of Kosmos, an encyclopaedic compilation of information about the physical world [Schwabe, 1851]. Suddenly, sunspots and their cycle became a hot topic: astronomers began counting sunspots and studying them, earlier cycles were reconstructed from old observations, and searches began for terrestrial effects which correlated with the sunspot cycle.

    Very soon such a correlation was found. Edward Sabine, a British scientist and the main architect of a worldwide network of magnetic observatories (an expansion of an earlier effort by Gauss and Weber), announced in 1852 that the frequency of magnetic storms rose and fell with the number of sunspots [Sabine, 1852; Meadows and Kennedy, 1982] (see also Lamont [1852]).

    The first serious study of this phenomenon was performed by the Norwegian Kristian Birkeland [Birkeland, 1901, 1908; Egeland, 1984,1986; Devik, 1968; Boström, 1968]. In 1896 Birkeland aimed cathode rays at a magnet and found that the magnet apparently "sucked in" cathode rays: he suggested that the Earth's field did the same to beams from the Sun. He communicated his findings to his former teacher, the French mathematical physicist Henri Poincaré, who showed that rather than being attracted, charged particles were guided by magnetic field lines [Poincaré, 1896]. Poincaré calculated the motion of an electron in the field of a magnetic monopole, a completely soluble problem, and found that the electron spiraled around a cone bounded by field lines, gradually losing headway until at a certain distance it was reflected backward [Rossi and Olbert, 1970, section 2.5; Mitchell and Burns, 1968].

Figure 1.   Birkeland's terrella

    Birkeland then built a large vacuum tank, placed in it a spherical magnet--like Gilbert he called it a terrella--and aimed at it beams of cathode rays (Figure 1). Bright spots appeared where the beams hit the terrella, generally in the polar regions. In some experiments there were even bright rings around the magnetic poles.

    By that time, appreciable information had accumulated about the aurora. Elias Loomis of Yale published a map of contours of equal auroral frequency in the northern hemisphere [Loomis, 1860], showing that they centered on the magnetic pole (rather than the geographic one) and that their frequency was highest in an oval band about 200 from the pole [Eather, 1980]. Hermann Fritz conducted a similar study with far greater precision [Fritz, 1881]. Following Birkeland's work the pieces suddenly seemed to fall into place: flares (or sunspots) apparently emitted electron streams, which were steered by the Earth's field toward the auroral zones--and since a stream of electrons carried an electric current, a magnetic disturbance would also be produced [Stoermer, 1917].

    This view was supported by Maunder [1904], who had deduced a tendency of storms to recur at 27-day intervals, the rotation period (relative to Earth) of low solar latitudes where sunspots tend to occur. He noted that recurrent storms were hard to correlate with solar phenomena (see further discussion below), but he still believed that "solar streams" were responsible and wrote as follows:

That, therefore, which Lord Kelvin spoke of twelve years ago as "the fifty years' outstanding difficulty" is now rendered clear. Our magnetic disturbances have their origin in the Sun. The solar action which gives rise to them does not act equally in all directions, but along narrow, well-defined streams, not necessarily truly radial. These streams rise from active areas of limited extent. These active areas are not only the source of our magnetic disturbances but are also the seats of the formation of sun-spots. . . .

    He did, however, manage to prove that a wide class of orbits existed in the dipole field that were trapped and did not extend to infinity. He furthermore showed that for sufficiently low particle energies all orbits hitting the terrella at low and middle latitudes were trapped, so that particles arriving from a distant source, like the electrons in Birkeland's experiment, never reached those latitudes but were always steered to the polar regions or turned away, in full accord with Birkeland's observations. In the Earth's field, Stoermer's theory worked well for cosmic ray particles in the Gev range, but not for auroral electrons. It was realized quite early that the atmospheric density at 100 km, where auroral electrons generally stopped, was so low that the energy of such electrons had to be low too. For instance, Harang [1951, table 31] estimated their speed at 0.3c, corresponding to about 23 keV. At such low energies, Stoermer's theory predicted impacts very close to the magnetic poles, contrary to observations that showed the midnight aurora peaked around magnetic latitude 68¡. Neither could it explain the observation that auroras were scarce near the magnetic pole itself.

    The theory of solar electron streams soon hit another snag: Arthur Schuster [Schuster, 1911; Chapman, 1934; Bartels 1934b] showed that electrostatic repulsion would quickly disperse any stream of solar electrons.