In the rotary drilling of oil wells a drilling mud is used both to transport the cuttings up to the surface and to impose an hydrostatic pressure on the walls of the borehole. For these functions the mud must for example have an acceptable viscosity and density. It is therefore important to monitor the characteristics of the mud, and to keep them within certain limits. Only recently, however, has drilling practice recognized the importance of monitoring the mud's ionic composition. The various techniques proposed involve separation of the mud into liquid and solid portions, and analysis of these. Though they have proven useful, yet there are a number of problems. For example, the separation has not always been easy, and the available techniques often may not satisfactorily remove the fines. The invention suggests that these two problems, at least, can be overcome by the relatively simple expedient of first acidifying the mud sample, for acidification both causes the mud particles to flocculate, and so be more easily separated off, and causes the active fines to dissolve. In a preferred embodiment hydrobromic acid is employed, together with tetramethylammonium bromide (a displacement agent enabling the mud solid's Cationic Exchange Capacity to be measured), the separation is by filtration, and the analysis is by ion chromatography--and the results are fed into a computer model that then calculates the original mud components.