The modern methods for the separation of these elements are based almost entirely on the differences in solubility of the various double nitrates.[239] The mixed double sulphates separated by saturation of a solution of the chlorides with sodium sulphate, which contain the cerium and most of the terbium elements, are transformed into nitrates, and the neutral solution boiled with potassium bromate, in presence of powdered marble, till all the cerium is precipitated as basic ceric nitrate. From the filtered solution the other elements are thrown down as oxalates, transformed into the magnesium double nitrates (A in Fig. 8), and fractionated from nitric acid solution[240] until a rough separation has been effected (fractions 1, 2, 3, and 4). The separation, which is somewhat long and tedious, is followed by means of the absorption spectra, and by the colour changes of the fractions. Fraction 1, containing lanthanum and some praseodymium, should be faint green to colourless; fraction 2 is colourless by the complementary action of the coloured salts of neodymium and praseodymium; fraction 3, which should contain the crude neodymium salt, is amethyst; and fraction 4, the mother-liquor, is yellow from the presence of the samarium compound. [239] The following scheme is largely from James, ‘The Separation of the Rare Earths,’ _J. Amer. Chem. Soc._ 1912, ~34~, 757. [240] See Demarçay, _Compt. rend._ 1900, ~130~, 1019 and 1186; also Drossbach, _Ber._ 1902, ~35~, 2826, and Muthmann and Weiss, _Annalen_, 1904, ~331~, 1. Fraction 1 is now converted to the double ammonium nitrates, which allow of a readier separation at this stage; two fractions are obtained, of which the less soluble, fraction 5, is the fairly pure lanthanum compound, whilst the more soluble, fraction 6, contains the praseodymium with a little lanthanum. The lanthanum ammonium nitrate, fraction 5, is converted into the anhydrous sulphate, which is dissolved in ice-water; when the solution is gradually warmed, the enneahydrate, La₂(SO₄)₃,9H₂O, separates, and may be obtained perfectly pure by recrystallisation. It is of interest that the radioactive element actinium is chemically very similar to lanthanum, and follows it closely through the process of separation. The mixed praseodymium and neodymium magnesium nitrates which constitute fraction 2 are transformed into the double manganese nitrates, and the crystallisation from nitric acid continued.[241] The less soluble part, fraction 7, is fairly free from neodymium, and the separation is continued with that of fraction 6, until both lanthanum and neodymium have been completely removed. The more soluble part, fraction 8, yields the pure neodymium compound, as does also the crude neodymium magnesium nitrate which constitutes fraction 3, if the crystallisation be continued. [241] Cf. Lacombe, _Bull. Soc. Chim._ 1904, [iii.], ~31~, 570.