(!Conc'n Ba^{++} x Conc'n SO_{4}^{--})/(Conc'n BaSO_{4}) = Const.!, and since !Conc'n BaSO_{4}! for the saturated solution has a constant value (which is very small), it may be eliminated, when the expression becomes !Conc'n Ba^{++} x Conc'n SO_{4}^{--} = Const.!, which is the "solubility product" of BaSO_{4}. If, now, an excess of the precipitant, a soluble barium salt, is added in the form of a relatively concentrated solution (the slight change of volume of a few cubic centimeters may be disregarded for the present discussion) the concentration of the Ba^{++} ions is much increased, and as a consequence the !Conc'n SO_{4}! must decrease in proportion if the value of the expression is to remain constant, which is a requisite condition if the law of mass action upon which our argument depends holds true. In other words, SO_{4}^{--} ions must combine with some of the added Ba^{++} ions to form [BaSO_{4}]; but it will be recalled that the solution is already saturated with BaSO_{4}, and this freshly formed quantity must, therefore, separate and add itself to the precipitate. This is exactly what is desired in order to insure more complete precipitation and greater accuracy, and leads to the conclusion that the larger the excess of the precipitant added the more successful the analysis; but a practical limit is placed upon the quantity of the precipitant which may be properly added by other conditions, as stated in the following note.] [Note 3: Barium sulphate, in a larger measure than most compounds, tends to carry down other substances which are present in the solution from which it separates, even when these other substances are relatively soluble, and including the barium chloride used as the precipitant. This is also notably true in the case of nitrates and chlorates of the alkalies, and of ferric compounds; and, since in this analysis ammonium nitrate has resulted from the neutralization of the excess of the nitric acid added to oxidize the iron, it is essential that this should be destroyed by repeated evaporation with a relatively large quantity of hydrochloric acid. During evaporation a mutual decomposition of the two acids takes place, and the nitric acid is finally decomposed and expelled by the excess of hydrochloric acid. Iron is usually found in the precipitate of barium sulphate when thrown down from hot solutions in the presence of ferric salts. This, according to Kuster and Thiel (!Zeit. anorg. Chem.!, 22, 424), is due to the formation of a complex ion (Fe(SO_{4})_{2}) which precipitates with the Ba^{++} ion, while Richards (!Zeit. anorg. Chem.!, 23, 383) ascribes it to hydrolytic action, which causes the formation of a basic ferric complex which is occluded in the barium precipitate. Whatever the character of the compound may be, it has been shown that it loses sulphuric anhydride upon ignition, causing low results, even though the precipitate contains iron.