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Resultate aus den Beobachtungen des magnetischen Vereins im Jahre 1836 [-1841]. [With:] Atlas des Erdmagnetismus nach den Elementen der Theorie entworfen. Leipzig: Weidmann, 1840.Göttingen & Leipzig: Dieterich & Weidmann, 1837-43.. All first editions.
Extremely rare complete set of the volumes, including the supplementary atlas volume, published by the Magnetischer Verein, "a society organized by Gauss and Weber which united a worldwide network of magnetic observatories and established an important precedent for international scientific cooperation" (Norman). We are not aware of any other complete set having appeared on the market, and there is no complete copy in auction records. The sets in most major collections, such as Honeyman, Norman, and Wheeler Gift, are incomplete.

❧Dibner 66; Norman 883; Wheeler-Gift 920; Honeyman 1456 (all having only the volumes of 1836-7 and the Atlas).

In 1828, while attending the Naturforscherversammlung, a three-week conference in Berlin, Gauss met Wilhelm Weber, a young German physicist who was conducting experiments with electromagnets. In April 1831 the professorship of physics at Göttingen, vacated upon the death of Tobias Mayer, Jr., was offered to Weber; and six years of collaboration and close friendship with Gauss followed. "As Gauss and Weber began their close collaboration and intimate friendship, the younger man was just half the age of the older. Gauss took a fatherly attitude. Though he shared fully in experimental work, and though Weber showed high theoretical competence and originality during the collaboration and later, the older man led on the theoretical and the younger on the experimental side" (DSB).

Gauss and Weber constructed a new magnetic laboratory, free of all metal that might affect magnetic forces (copper rather than iron nails held it together). In 1834 there were twenty-three magnetic observatories in Europe, and it was Humboldt's desire to have these observatories collaborate. His vision began to be realized when Gauss and Weber established the Magnetischer Verein (Magnetic Union). "Its Resultate aus den Beobachtungen des magnetischen Vereins appeared in six volumes (1836-1841) and included fifteen papers by Gauss, twenty-three by Weber, and the joint Atlas des Erdmagnetismus (1840). These and other publications elsewhere dealt with problems of instrumentation (including one of several inventions of the bifilar magnetometer), reported observations of the horizontal and vertical components of magnetic force, and attempted to explain the observations in mathematical terms. The most important publication in the last category was the Allgemeine Theorie des Erdmagnetismus (1839). Here Gauss broke the tradition of armchair theorizing about the earth as a fairly neutral carrier of one or more magnets and based his mathematics on data. Using ideas first considered by him in 1806, well formulated by 1822, but lacking empirical foundation until 1838, Gauss expressed the magnetic potential at any point on the earth's surface by an infinite series of spherical functions and used the data collected by the world network to evaluate the first twenty-four coefficients. This was a superb interpolation, but Gauss hoped later to explain the results by a physical theory about the magnetic composition of the earth. Felix Klein has pointed out that this can indeed be done (Vorlesungen über die Entwicklung der Mathematik im 19. Jahrhundert [Berlin, 1926], pt. 1, p. 22), but that little is thereby added to the effective explanation offered by the Gaussian formulas" (ibid.). In the Allgemeine Theorie des Erdmagnetismus, Gauss and Weber also proved that there can only be two magnetic poles on earth - a North Pole and a South Pole. They theoretically determined the location of the magnetic South Pole and concluded that it did not coincide with the geographic South Pole. Sailors confirmed that the locations of the magnetic poles found by Gauss and Weber were very nearly correct.

The Resultate for the year 1839 contains, among seven other papers, Gauss's important theoretical paper 'Allgemeine Lehrsätze in Beziehung auf die im verkehrten Verhältnisse des Quadrats der Entfernung wirkenden Anziehungs - und Abstossungs-Kräfte,' "the first systematic treatment of potential theory as a mathematical topic, [which] recognized the necessity of existence theorems in that field, and reached a standard of rigor that remained unsurpassed for more than a century" (DSB V 306). "Here Gauss formally introduced the term 'potential' to designate the function from which the components of forces varying as the inverse square of the distance can be derived. He wrote the function as V = Σ μ/r, which expresses the action at any point of a collection of point 'masses' or, in general, 'agents', and he developed a collection of theorems concerning the behavior of this function. The significance of V is that its properties are the 'key to the attracting or repelling forces' of nature. Potential theory applies to the phenomena of nature described by inverse-square forces between particles, to the phenomena of gravitation, electricity and magnetism. Gauss even considered its application to electrodynamic phenomena, since Ampère's force between current elements depends on the inverse square of the distance; but the action of this force is complicated by the directionality of currents, and Gauss did not treat it here and only spoke of discussing it in a later paper, which he never did.

"Gauss showed that despite the striking differences of the observed phenomena of gravitation, electricity and magnetism, their mathematical description draws on a common body of theorems. Potential theory provided mathematical methods of impressive generality: by studying the behavior of one function, abstracted from any one domain of phenomena, physicists could learn at once the mathematical structures relating the phenomena belonging to several domains. The conservation of energy principle, enunciated soon after Gauss's potential theory, made the potential an even more important aid in developing physical laws" (C. Jungnickel & R. McCormmach, Intellectual Mastery of Nature. Theoretical Physics from Ohm to Einstein (1990), pp. 68-9).

The Atlas des Erdmagnetismus was the most important set of geomagnetic charts published up to that time. On two of these charts, equipotential lines were presented for the first time in history.. Göttingen: Dieterichschen Buchahndlung & Leipzig: Weidmann'sche Buchhandlung, 1837-1843. 8vo (210 x 130 mm), pp. [2], 103, [21]; iv, 140, [63]; vi, [2], 150, [72]; iv, 130, [58]; iv, 174, [84]; iv, 133, [142], with 50 engraved plates (30 folded and 18 double-page). [With:] Atlas des Erdmagnetismus nach den Elementen der Theorie entworfen. Leipzig: Weidmann, 1840. 4to (271 x 225 mm), pp. IV, 36, with 18 double-page maps and 4 double-page tables. Together nine volumes (the plates for the 1838 and 1841 Resultate bound separately (as issued), these plates with some spotting and browning but much less than is usually found. Contemporary half-cloth (plates for 1838 and 1841 bound in original boards rebacked with old paper). In all a very fine and exceptionally rare complete set

      [Bookseller: Sophia Rare Books]
Last Found On: 2015-03-09           Check availability:      Antikvariat    

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