In the previous progress report (Trudgill and Briggs, 1977) a key problem area emerged, that of the difficulties of the accurate measurement of field soil processes. Moreover, while precise mathematical models may be derived to describe soil processes it is often difficult to allow for the variability and irregularity of natural processes. Nevertheless, in the year succeeding the last report, definite progress has been made both in mathematical modelling and in experimental work. Several research publications have appeared where the abstract models are more detailed and thus more realistic. Also, the experimental research is reinforcing a trend of improved field and laboratory measurements and of allowing for natural variations of factors.In addition to individual research publications, some useful review papers have also appeared. A paper by Arnold (1977) highlights the search for unifying concepts in soil science. Professor Arnold sees three needs for unifying concepts; firstly to make empirical work less empirical; secondly, to bring apparently disconnected pieces of information together; and thirdly, to bring the particular towards the general. While he concludes that the search goes on and there are, as yet, few unifying concepts, his focus of attention is on the identification of the critical area of I nm size between solid and solution. A knowledge of this area, he maintains, is fundamental to the understanding of soil formation, soil-soil solution-plant interactions, soil-pollutant processes and soil management. This area of concern is again highlighted ,by the historical review of Thomas (1977). Here, the problem is seen that in ion exchange processes work on complex, natural substances has not kept pace with work in purer substances. For example, non-crystalline Al and Fe may determine cation exchange behaviour in soils and the study of the behaviour of pure clay minerals does not predict soil clay characteristics because of the inclusion of non-crystalline amorphous forms in soil clays.It is perhaps because of the clear identification of a central concern with solid: solution reactions and the simultaneous awareness of the difficulties of studying and predicting the behaviour of the reactions in real soils that mathematical modelling continues to be useful. For example, Leistra and Dekkers (1977) have published a paper on computed effects of adsorption