Brauner criticises these values on the ground that no details are given as to the temperature required to obtain the anhydrous salt from the hydrates, and that probably some traces of sulphate must be decomposed at the temperatures required (450°-500°) to drive off all the water. The results obtained from the enneahydrate are to a great extent invalidated by the doubts as to the purity of the hydrate, completeness of dehydration, etc., which arise from the discrepancies in the values deduced from the three ratios. He accepts, however, the figure 232·49 obtained by Nilson and by Krüss and Nilson from material separated as octohydrate, with some uncertainty as to the second decimal figure. Brauner himself employed the oxalate method in 1898; the purified hexahydrate was used, the percentage of thoria being determined by ignition, and of (C₂O₃) by titration with permanganate. The ratio ThO₂ : 2C₂O₃ gave results varying from 232·21 to 232·29, but as the value rose continuously as purification was carried further and further, he did not feel justified in taking a mean value. In 1900 Urbain determined the constant with material purified by the acetylacetone method. He prepared the octohydrate, heated it for ten hours in a bath of sulphur vapour at 440°, and ignited the anhydrous salt so obtained at a white heat. The ratio ThO₂ : 2SO₃ gave the result (corrected to vacuo) Th = 233·67. Brauner criticises the value on the ground that the hydrated salt was heated in a vessel open to the air, and that at the high temperature obtained, traces of moisture gaining access to the sulphate caused hydrolysis, with loss of sulphuric acid; this would cause the results to be too high. In 1905 Meyer and Gumperz employed the same method, and obtained values varying from 232·2 to 232·7, with the mean 232·47. Finally Brauner carried out an extended investigation to disprove the heterogeneity of thorium which had been ‘discovered’ by Baskerville (1904), in the course of which he showed the atomic weight of the element to lie between the limits 232·34 and 232·52. ~Detection of Thorium.~--The element is best detected in a mixture of earths by the following reactions: (1) Precipitation with hydrogen peroxide from warm, faintly acid solution. (2) Precipitation with sodium hypophosphate, Na₂H₂P₂O₆, in concentrated hydrochloric acid solution. On boiling, a perceptible precipitate is obtained if only traces of thorium are present; but ceric and zirconium salts and titanium must be absent. The latter element gives no precipitate under these conditions if hydrogen peroxide is present; ceric salts may be decomposed by boiling. The possible presence of zirconium renders it necessary to boil the hypophosphate precipitate with nitric acid; on addition of oxalic acid to the clear solution, thorium is precipitated, whilst zirconium remains in solution, and may be detected.