
10. Gauss and the Global Magnetic Field 
Index 8. Oersted & Ampére 9. The Lodestone 10. Gauss 11. The Magnetic Sun 12. Fluid Dynamos 13. Dynamo in the Earth's Core 14. Magnetometers and Tobacco Smoking 15. Magnetic Reversals & Moving Continents 16. The Magnetosphere 17. Magnetic Planets 
Public interest in science owes a great deal to Alexander Von Humboldt (17691859). As a young man Alexander explored the jungles of South America, but much of his life was spent in Paris, where he tirelessly drew the public's attention to the achievements of the natural sciences. Late in life he assembled his scientific knowledge into a monumental set of volumes titled " Kosmos."
Up to that time, the compass needleand the downwardpointing "dip needle" on a horizontal axismeasured well the direction of the magnetic force, but what about measuring its strength? Gauss devised a clever method for doing so, using an auxiliary magnet; today this is a popular undergraduate lab excercise. 
He also knew a method used in celestial mechanics for analyzing gravity, and applied it to the description the Earth's region of magnetic forces, its "magnetic field." That method, too, is still in use: it represents the field as the sum of a dominant northsouth "dipole" (2pole, like a bar magnet) whose strength decreases with distance r like 1/r^{3}, plus a "4pole" decreasing like 1/r^{4}, plus an 8pole decreasing like 1/r^{5}, and so forth. The field of an isolated "monopole" would presumable decrease like 1/r^{2}, the way gravity doesbut no such single pole was ever observed, they always come (at the very least) in pairs. The new tools for better observation and description of the Earth's magnetic field led to better, worldwide observations. Gauss and Weber organized a "Magnetic Union" for setting up observatories, and Humboldt enlisted Russia's Czar to create a chain of them across Siberia. The greatest help however came from the British empire, whose "Magnetic Crusade" led by Sir Edward Sabine set up stations from Canada to Tasmania (then known as "Van Diemen's Land"). The vast network not only made possible the first global models of the field, but also demonstrated the worldwide character of magnetic storms. One can compare today's magnetic models, some of them based on satellite observations, to the ones started by Gauss more than 150 years ago. One trend then stands out: the dominant "dipole" field is getting weaker, at about 5% per century (the rate might have increased since 1970). In the unlikely event that the trend continues unchanged, about 15002000 years from now the magnetic polarity of the Earth would reverse. Further ExplorationIn the mathematical description of magnetic fields, the magnetic flux through some given area is an important concept. The prescription for deriving the flux entering the areahere, core surfaceis(1) divide the area into patchesthose where field lines enter and those where where they leave. (2) Ignore the latter areas. Divide the area where the lines enter into small subareas. (3) Multiply each subarea by the component of the magnetic vector perpendicular to the surface, and (4) Add all products together. What you get is the magnetic flux entering the core.
If you had done the same with areas where field lines exit from the core, it can be shown that you would have got the same result, but with minus sign, denoting flux leaving instead of entering. If you ignore the sign and mark every contribution as positive, you get exactly the same flux. Calculating the "total unsigned flux" at the core surface gives the sum of the twothe "total unsigned flux," equal to twice the entering magnetic flux, and therefore, also (very very nearly) unchanged with time. The "total unsigned flux" is however easier to derive (which is why geomagneticians prefer working with it), because you no longer need to divide the surface into irregular patches of incoming and outgoing field linesevery bit of area is used in the calculation.
"Carl Friedrich Gauss, Titan of Science"This definitive biography of Gauss by Waldo G Dunnington, 479 pp., was first published in 1955. Republished in 2004 by the Mathematical Association of America, with an addition by Jeremy Gray as well as a contribution by FritzEgbert Dohse, bringing the page count to 586.Tidbit. Gauss had 6 children, and he quarreled with one son over the cost of a party which Gauss refused to pay. In protest, the son left Germany in 1830 and joined the US army. After ending his service, he settled in Missouri and was joined there by a brother; as a result, many of Gauss'es descendants today live in the US. Back to the Master List 