In the double sulphate separation of the yttrium and cerium groups, the terbium elements divide themselves between the soluble and the insoluble portions; if the separation is made as complete as possible by addition of a large excess of alkali sulphate under suitable conditions, the larger part of the compounds of the group will be precipitated with the cerium elements. In the separation of the cerium elements the terbium elements collect in the most soluble fractions, and the mother-liquors of the double nitrate crystallisations therefore form a very convenient source of these elements. A considerable proportion, however, will usually remain in solution with the double sulphates of the yttrium group; in the bromate separation of these (see p. 198), the terbium elements collect in the least soluble fractions. By careful fractionation under suitable conditions, the double sulphate method may be used to separate the terbium group completely from the cerium and yttrium elements. A very convenient method of separating the terbium group from a rare earth mixture is the ethylsulphate process of Urbain. By fractional crystallisation of these salts from alcohol or water, the separation into three groups can be satisfactorily accomplished. For the separation of the terbium elements from one another, the nitrate and double nitrate methods are most suitable. Samarium can readily be separated by crystallisation of the double magnesium nitrates in presence of bismuth magnesium nitrate; by continuing the fractionation, europium magnesium nitrate can be separated in a pure state, as there is a considerable difference between the solubility of this salt and the corresponding compound of gadolinium;[311] the process, however, is somewhat long and tedious. For the separation of gadolinium and terbium, the double nitrates are converted into the simple nitrates, and these fractionated from nitric acid in presence of bismuth nitrate. The gadolinium nitrate separates before the bismuth nitrate, and may be obtained fairly pure in this way, though the process is extremely tedious, and several thousand recrystallisations are required.[312] Terbium nitrate has almost the same solubility as bismuth nitrate, and the two separate together in the middle fractions. The more soluble nitrates of the erbia earths collect in the mother-liquors. [311] James (_J. Amer. Chem. Soc._ 1912, ~34~, 757) employs at this stage the fractional crystallisation of the double nickel nitrates. [312] See Urbain, _Compt. rend._ 1904, ~139~, 736. ~Europium~, Eu = 152·0