The initial aim of this research was to use empirical mathematical relationships to formulate a better understanding of the processes involved in the liquefaction of a set of medium rank high sulfur coals. In all, just over 50 structural parameters and yields of product classes were determined. In order to gain a more complete understanding of the empirical relationships between the various properties, a number of relatively complex statistical procedures and tests were applied to the data, mostly selected from the field of multivariate analysis. These can be broken down into two groups. The first group included grouping techniques such as non-linear mapping, hierarchical and tree clustering, and linear discriminant analyses. These techniques were utilized in determining if more than one statistical population was present in the data set; it was concluded that there was not. The second group of techniques included factor analysis and stepwise multivariate linear regressions. Linear discriminant analyses were able to show that five distinct groups of coals were represented in the data set. However only seven of the properties seemed to follow this trend. The chemical property that appeared to follow the trend most closely was the aromaticity, where a series of five parallel straightmore » lines was observed for a plot of f/sub a/ versus carbon content. The factor patterns for each of the product classes indicated that although each of the individual product classes tended to load on factors defined by specific chemical properties, the yields of the broader product classes, such as total conversion to liquids + gases and conversion to asphaltenes, tended to load largely on factors defined by rank. The variance explained and the communalities tended to be relatively low. Evidently important sources of variance have still to be found.« less