  Motivated by a property of linear resistive electrical networks, we introduce
the class of Rayleigh matroids. This is a subclass of the balanced matroids
introduced by Feder and Mihail [FM] in 1992. We prove a variety of results
relating Rayleigh matroids to other well-known classes -- in particular, we
show that a binary matroid is Rayleigh if and only if it does not contain S_8
as a minor. This has the consequence that a binary matroid is balanced if and
only if it is Rayleigh, and provides the first complete proof in print that S_8
is the only minor-minimal binary non-balanced matroid, as claimed in [FM]. We
also give an example of a balanced matroid which is not Rayleigh.
