In presence of a large excess of alkali carbonate, double carbonates are formed. The stability as well as the solubility of these compounds increases in passing from the cerium to the yttrium group, _i.e._ as the electropositive character becomes weaker. The double carbonates of the cerium elements are sparingly soluble, and are decomposed by water, especially on warming; they may, however, be recrystallised from alkali carbonate solution. The sodium and ammonium double salts are less soluble than the potassium compounds. The latter have the general formula R₂(CO₃)₃,K₂CO₃,12H₂O, and are of considerable importance in many processes of separation. The yttrium elements can be separated from the cerium metals, and the latter from one another, by taking advantage of the differences of solubility shown by the potassium double carbonates. If a concentrated solution of the salts in potassium carbonate solution be fractionally diluted with water, the cerium elements separate in the order: lanthanum, praseodymium, cerium, neodymium, and samarium; the more soluble yttrium compounds remain in the solution. Thorium forms double alkali carbonates which are very readily soluble in excess of alkali carbonate; this property is of great importance for the technical separation of the element. ~Oxalates.~--The oxalates of the rare earth elements are of the greatest importance, on account of the fact that they are not only insoluble in water, but are also very sparingly soluble in dilute mineral acids, and in excess of oxalic acid. They can be completely precipitated even from strongly acid solutions by addition of sufficient excess of oxalic acid, or alkali oxalate, and thus afford a means of easily and completely separating the rare earth group from the commoner elements. They are thrown down by addition of oxalic acid, or alkali oxalate, as amorphous precipitates, which rapidly become crystalline, especially if the solution is warmed. From water at normal temperatures they usually separate as the decahydrates, R₂(C₂O₄)₃,10H₂O, but hydrates with 7, 9, and 11 molecules of water of crystallisation are also known. From strongly acid solutions, mixed oxalo-salts of the general formula R(C₂O₄)X, where X = Cl, NO₃, HSO₄, etc., may be obtained. These mixed salts may also be prepared by dissolving the oxalates in concentrated solutions of the chlorides, nitrates, etc., whilst nitro-sulphates, R(SO₄)NO₃, have been obtained by recrystallising the sulphates from strong nitric acid. The tendency to form salts with mixed acid radicles appears to be general.[166] [166] See Meyer and Marckwald, _Ber._ 1900, ~33~, 1003; also Matignon, _Ann. Chim. Phys._ 1906, [viii.], ~8~, 243.