A magnetic system on the sites (j/n;j=1,...,n) of the circle T approximately=R (mod 1) is studied in the limit n to infinity . The interaction is defined in terms of a continuous function J(x, y),x,y in T. For any ferromagnetic J(J>0) which satisfies a normalisation condition, the thermodynamic behaviour is identical to that of the Curie-Weiss model (J identical to 1). This simple case is in contrast to the behaviour for a class of translation invariant, non-ferromagnetic J, for which a continuum of equilibrium states exists for sufficiently low temperatures. In both cases a probabilistic interpretation of the equilibrium states is given.