This question is a continuation of my previously-posted question: [Several questions about Gauss's contributions to electromagnetism](https://hsm.stackexchange.com/questions/7503/several-questions-about-gausss-contributions-to-electromagnetism?noredirect=1#comment13789_7503). I wrote it after user vonbrand asked me to split my original question into several.
I'm very interested to learn about Gauss's unpublished fragments on electromagnetism; especially i'm interested in Gauss's "Zur Electrodynamik" (Gauss's werke, volume 5, p. 601 - 630).

The first titles in this manuscript relate directly to electric circuits, and 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 (titles 1-2) and p. 621-622 (titles 16-17)**), which i didn't find comments about in the literature. The formulas related to these figures seem to be of a very interesting form (they involve uncommon functions in the basic theory of electric circuits). For these reasons, i refuse to believe that nobody knows what these figures describe, so if anyone knows something about these schematic figures, please explain.

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 - Gauss writes: "The basic principle is that $\sum ri^2$ is in minimum for the actual current distribution". Here, $r$ is the resistence of a resistor and $i$ the electric current (for explanation see this article: [The Minimum Entropy Production Principle](https://bayes.wustl.edu/etj/articles/min.ent.prod.pdf)). So, did Gauss refer to this important **variational principle** in several of his letters (to Weber, perhaps?)?