150Th Anniversary of Gauss's First Absolute Magnetic Measurement

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Nature Vol. 297 27 May 1982 285 and the age estimates based on com pared with star cluster ages which are both Mand H can readily be deduced. parative abundances of radioactive nuclei. estimated to be in excess of ten billion Because of secular change, it is difficult This would at least avoid the problems years. The lower value of 50 km s- 1 Mpc- 1 to assess the accuracy of Gauss's original created by the higher value of H0 of cannot be ruled out, although the age of observation but, from internal consistency 100 km s-1 Mpc-1 , which suggests a galaxies (following Osmer's result) would and backward extrapolation of the trend Universe age of nine billion years com- have to be at least 14.5 billion years. D from later observations, it seems likely that it was within one per cent of the true value. With only minor modifications, Gauss's method continued to be the standard way of measuring Hat magnetic observatories and in the field until the 1920s, and it is still 150th anniversary of Gauss's in use at some observatories. Nowadays, first absolute magnetic measurement absolute magnetic intensity measurements are usually made with a proton magneto from S.R.C. Malin and D.R. Barraclough meter. This gives the answer to an accuracy of about l part in 1()6 in a few seconds. ON 26 May 1832, the horizontal months later, after Gauss had slightly This was not Gauss's only contribution component of the Earth's magnetic field at revised his dimensional arguments. The to geomagnetism. He later applied yet Gottingen was 1.7820 mgY'mm-'10 s-1 apparatus required is very simple - two another of his inventions, the method of ( = 17,820 nT). Not particularly remark bar magnets (A and 8), one single-filament spherical harmonic analysis, to the Earth's able, you might think, except that this was suspension in which either magnet can be magnetic field to show that nearly all of it the first ever absolute measurement of the fitted, a ruler, a clock and two weights. The came from inside the Earth. He was also, geomagnetic field and its attainment had method is also simple, though a number of with Humboldt, largely responsible for the required much of the armoury of one of the refinements are required if its full accuracy 'Gottingen Magnetic Union', an inter world's greatest mathematicians. is to be realized. The first part is the national project for the simultaneous Carl Friedrich Gauss (1777-1855) was a vibration experiment in which magnet A is observation of the magnetic field on four gifted child. His early mathematical feats suspended horizontally, and its period of selected term-days each year at a number of led his father grudgingly to agree with his oscillation either side of magnetic north widespread sites. This scheme developed teachers that the boy should receive higher measured. The period T is related to the into the worldwide network of magnetic education rather than learn a trade, but magnet's moment of inertia, I, its magnetic observatories that exists today. D Gauss was also an exceptional linguist and moment, M, and the horizontal intensity of might equally easily have chosen to study the geomagnetic field, H, by philology. It was the satisfaction he derived in 1796 from demonstrating the con T=2TI r- struction of a regular 17-sided polygon :;;;; with ruler and compasses that finally Thus, if I is known, we can infer M H. decided him on a career in mathemtics. In Gauss deduced I by adding known his doctoral thesis, he proved the increments to it in the form of weights at 'fundamental theorem ofalgebra' (the first known distances from the suspension, and of his four independent proofs of this noting how this affected T. In calculating I theorem), and most of his work at this time from the several different values of T and (a) was similarly concerned with pure ~ I, Gauss used a powerful technique mathematics. Although this continued to which he had developed himself, the be his main interest, he gradually branched method of least squares. He also took care out into many other subjects, including to adjust Tto the value it would attain with applied mathematics, astronomy, geodesy, vibrations of infinitesimal amplitude, as optics, telegraphy and geomagnetism. the equation is strictly valid only for that Soon after 1830, Gauss became in case. terested in the adoption of a universal The second part is the deflection system of units for all physical quantities, experiment in which the ratio MIH is and came to the remarkable conclusion determined by suspending magnet B and that even magnetic intensity could be noting its angular deflection from measured in terms of mass, length and magnetic north when magnet A is placed at time. With the practical assistance of a known distance to the east or west. This Wilhelm Weber, professor of physics in the requires a knowledge of the way in which University of Gottingen, he set about the magnetic intensity due to a bar magnet devising an experiment to make this falls off with distance. Gauss deduced this measurement. He explains some of his from first principles, showing not only that Gauss's experiment. (a) The vibration ex ideas in a letter to the astronomer Olbers the intensity due to a dipole depends on the periment. The magnet, A, suspended by a written on 18 February 1832. inverse cube of the distance, but also that silk thread, F, oscillates in a horizontal one additional term is both necessary and "I occupy myself now with the Earth's plane. Its moment of inertia can be varied magnetism, particularly with an absolute sufficient to allow for the finite length of by hanging weights, W, from the rod, R. determination of its intensity. Friend Weber the bar magnet. He determined the The period of oscillation is obtained by conducts the experiments on my instructions. parameters by measuring the deflection observing the reflection of the scale, S, in As, for example, a clear concept of velocity can with magnet A at different distances, again mirror M, through the telescope, T, and be given only through statements on time and solving by the method of least squares. timing an integral number of swings with space, so in my opinion, the complete From a knowledge of M Hand MIH, the clock, C. (b) The deflection experi determination of the intensity of the Earth's ment. Magnet B is suspended and is magnetism requires to specify (I) a weight= p, deflected from magnetic north by placing (2) a length= r, and then the Earth's magnetism S.R.C. Malin and D.R. Barraclough are in the magnet A at a known distance. The deflec can be expressed by vp/r." Institute of Geological Sciences, Murchison tion is measured by observing the reflec House, West Mains Road, Edinburgh EH9 tion of the scale, S, in mirror M, through The experiment came to fruition three 3LA. the telescope, T.