Acidify with hydrochloric acid the filtrate from the separation of calcium and concentrate it to about 100 cc. Add 20 cc. of a saturated solution of microcosmic salt, cool, and make slightly but distinctly alkaline by adding ammonium hydroxide, drop by drop. Allow the solution to stand four hours, then filter and wash with 3 per cent ammonium hydroxide. Dissolve the precipitate, especially in the presence of large amounts of sodium or potassium, in a slight excess of dilute hydrochloric acid and reprecipitate the magnesium with ammonium hydroxide and a few drops of microcosmic salt solution. If great accuracy is not required this solution and reprecipitation may be omitted. Ignite the precipitate and weigh it as magnesium pyrophosphate (Mg_{2}P_{2}O_{7}), 21.9 per cent of which is the equivalent of magnesium (Mg.). If manganese is present[64a] it is precipitated with the magnesium and a correction for it should be applied after having determined manganese in a separate sample. The weight of manganese pyrophosphate (Mn_{2}P_{2}O_{7}) is 2.58 times the weight of manganese. SEPARATION OF SULFATE, SODIUM, AND POTASSIUM. SULFATE. Evaporate to dryness 100 to 1,000 cc. of the sample, or sufficient to obtain a residue weighing 0.4 to 0.6 gram and containing preferably 0.05 to 0.2 gram of sodium. Acidify the residue with hydrochloric acid and remove the silica, iron, and aluminium (pp. 56–57). Make acid and add a hot solution of barium chloride in slight excess to the hot filtrate, and warm it, stirring at intervals for one-half hour, until the precipitate settles readily and leaves a clear supernatant liquid. Dry, ignite, and weigh the precipitate of barium sulfate, 41.1 per cent of which is equal to the content of sulfate (SO_{4}). SODIUM, POTASSIUM, AND LITHIUM.