In his books, Tutte tells often of how he and his friends in Cambridge introduced a theory of non-symmetric electricity. His tales are always amusing and enjoyable, but often lack precise references; it does not help, either, that he often published his articles in journals that have little or no internet visibility nowadays.

In particular, I am trying to track back his version of the Matrix-Tree Theorem for digraphs, which makes use of the so-called Kirchhoff matrix - basically, the diagonal matrix of the outdegrees minus the outgoing adjacency matrix, but I am incredibly stuck with his books (it is Theorem VI.27 of his "Graph Theory" book from 1984, for instance). But I cannot believe the theorem is so young. Concerning the Kirchhoff matrix itself, it seems to appear in "The dissection of equilateral triangles into equilateral triangles" from 1948. Maybe even earlier?

Can anybody help?