~Purification of the Thorium Compounds.~--The object of this last stage is to remove from the thorium compound small quantities of cerium and yttrium salts which cannot be separated by the carbonate method. The chief process is the sulphate crystallisation, the principles underlying which have been thoroughly examined in the patient researches of Koppel and Holtkamp.[503] Since the process is based on the solubilities of the various thorium sulphate hydrates, it is necessary to consider these in some detail. [503] _Zeitsch. anorg. Chem._ 1910, ~67~, 266. The solubility-curve of thorium sulphate was examined by Demarçay and by Roozeboom. Three important hydrates are known, viz. Th(SO₄)₂,9H₂O, Th(SO₄)₂,8H₂O, and Th(SO₄)₂,4H₂O, other unstable intermediate compounds being said to exist. From a study of the diagram it will be seen that the hydrate with 8 molecules of water is labile, whilst the 9-hydrate and the 4-hydrate have a transition temperature at 43°C., the transition temperature of the 8-hydrate and the 4-hydrate being just below this. [Illustration: FIG. 10] Since the 8-hydrate is labile with regard to the 9-hydrate, and the transition temperatures are so near, the former will be formed first as a solution cools, and by reason of the great similarity of the solubility-curves for the 9- and 8-hydrates the rate of change of this to the 9-hydrate will be very slow. In practice, therefore, it is always the 8-hydrate which is formed, and it is on the separation of this compound that the success of the process depends. The anhydro-compound, Th(SO₄)₂, which can be obtained by heating any of the hydrates to 300°-400°C., is very soluble at 0°, but slowly hydrates itself and separates from the solution as the 8-hydrate, which has a very low solubility. The sulphates of the cerium metals, compounds of which form the chief impurities to be removed, are considerably more soluble, and can be separated by repeated crystallisations.