For pt.I see Found. Phys., vol.9, no.11-12, p819-29 (1979). A general assumption made in a previous paper is modified by the elimination of the metrical entropy in favour of empirical entropy. Without reference to absolute temperature or metrical entropy, one then arrives at a generic form of the canonical probability in phase in which temperature does not occur. It is argued that this is as it should be if one looks upon the canonical ensemble as merely being the representative of a system in thermal equilibrium with its surroundings. One motivation for this work is to take a view of 'statistical mechanics' which does away with probabilistic notions altogether.