This paper addresses methodological issues in diachronic data analysis for historical research. We apply two families of topic models (LDA and DTM) on a relatively large set of historical newspapers, with the aim of capturing and understanding discourse dynamics. Our case study focuses on newspapers and periodicals published in Finland between 1854 and 1917, but our method can easily be transposed to any diachronic data. Our main contributions are a) a combined sampling, training and inference procedure for applying topic models to huge and imbalanced diachronic text collections; b) a discussion on the differences between two topic models for this type of data; c) quantifying topic prominence for a period and thus a generalization of document-wise topic assignment to a discourse level; and d) a discussion of the role of humanistic interpretation with regard to analysing discourse dynamics through topic models.