Several questions about Gauss's contributions to electromagnetism

Question

First of all, i appologize if i'm asking too many questions about Gauss (and some will also say "not very interesting questions"); i know i might appear ridiculus - but i really think it's an important goal to map the entire Gaussian contributions to math and science. Now, to my questions.

I'm very interested to learn about Gauss's unpublished fragments on electromagnetism; especially i'm interested in Gauss's "Zur Electrodynamik" (Gauss's werke, volume 5, p. 601 - 630).

• Electric circuits - The first titles in this manuscript record, to my opinion, his discovery of Kirchoff's laws for branched electrical circuits. But in addition, it seems that he studies some interesting configurations for electrical circuits (see p.601-604), which i didn't find comments about in the literature. So if anyone knows something about these schematic figures, please explain. By the way, it seems also that title 2 in this manuscript records his discovery of the "principle of minimum heat" (established by Kirchoff in 1848; it's related to minimum entropy principles), which Dunnington mentions in p.161 of his biography of Gauss.
• electromagnetic telegraph - was Gauss-Weber's telegraph just a combination of already known principles (binary code,...) and components (electrical wires,commutator)? or did they make essential improvements over these components?
• Sympathetic vibrations - Dunnington tells in his biography: "In 1834, he constructed an induction coil, and was enable to recognize the damping of a magnet vibrating in a coil as a result of induced currents; this led him to the construction of a copper damper for his magnetic apparatus, and to the discovery of "sympathetic vibrations"". I didn't find any comment about "Gauss's discovery of sympathetic vibrations" in the whole literature, and i'm curious to learn more of this.
• Mathematical descriptions for induction and electrodynamics - there is much more material in "Zur electrodynamics" according to Dunnington: "Grassmann's law", "Newmann's law of potential". If anybody knows something about these, i'll be glad to hear.

Thanks sincerely for all the efforts.

Answer 1

As for the third question (on "sympathetic vibrations"), p. 127-136 of Schaefer's treatise are the best source on this. According to these pages, much of Gauss's experimental investigations on magnetism was concerned with the determination of the magnetic moment of needles by measuring their period of oscillation; his main objective was to use such precise measurements to determine the constants of the different versions of his magnetometer (unifiliar and bifilar) and thus help measure the components of the earth's magnetic field. In the course of these investigations Gauss attempted to solve two "core" problems:

• The damping of oscillation of magnetic needle in the presence of a coil around it; the movement of the needle creates changing nagnetic field and thus induces current in the coil so it losses energy as a result (see Gauss's werke, volume 11, p.67-68 - "calculation of damped movements of the magnetic needle" ).
• The problem of mixed oscillations - Gauss attempted to describe the "collective oscillation" of several needles placed next to each other (see Gauss's werke, volume 11, p.63-65) . This is the context at which he discovered "sympathetic vibrations". There are additional details on this in his letters. Schaefer comments on this:

Gauss hat in diesen Versuchen die Theorie der erzwungenen Schwingungen eines Massenpunktes auf die induzierten Schwingungen des Magnetometers gewendet; anscheinend ist er der erste oder jedenfalls einer der ersten, der überhaupt das mechanische Problem der erzwungenen Schwingungen behandelt hat. Auffällig ist es, dass Gauss den allgemeineren Fall, den er im Briefe an Olbers andeutet, nämlich den, dass die »kleineren Nadeln« eine Rück- wirkung auf die grosse Nadel ausüben, nicht behandelt hat; er hat sich offenbar damit begnügt, durch Rechnung festzustellen, dass in seinem Falle diese Rückwirkung unmerkbar klein war; er hätte sonst das Phänomen der Schwebungen und das Hin- und Herpendeln der Energie finden müssen.

and in english this passage translates to:

Gauss, in these experiments, turned the theory of the forced vibrations of a mass point to the induced oscillations of the magnetometer; he seems to be the first, or at least one of the first, to deal with the mechanical problem of forced vibrations. It is remarkable that Gauss did not deal with the more general case he suggests in the letter to Olbers, namely, that the "smaller needles" have an effect on the big needle; he was evidently content to ascertain by calculation that in his case this repercussion was imperceptibly small; otherwise he would have had to find the phenomenon of beating and the oscillation of energy.

The whole picture of this aspect of Gauss's work is still not very clear to me (as there is so few information on it), so i posted this "answer" just to make some advance.