  The theoretical basis of continuum percolation has changed greatly since its
beginning as little more than an analogy with lattice systems. Nevertheless,
there is yet no comprehensive theory of this field. A basis for such a theory
is provided here with the introduction of the Potts fluid, a system of
interacting $s$-state spins which are free to move in the continuum. In the $s
\to 1$ limit, the Potts magnetization, susceptibility and correlation functions
are directly related to the percolation probability, the mean cluster size and
the pair-connectedness, respectively. Through the Hamiltonian formulation of
the Potts fluid, the standard methods of statistical mechanics can therefore be
used in the continuum percolation problem.
