The ratio of the manganese to the available oxygen was determined in the following manner. The contents of the flask were filtered through asbestos and the flask and the precipitate washed with cold water. The contents of the filter were then returned to the flask and treated with an excess of a standard solution of oxalic acid and dilute sulphuric acid. After reduction the excess of the oxalic acid was determined by a standard solution of potassium permanganate. The solution was then filtered, well washed and the manganese in the filtrate precipitated by the method of Gibbs. From the total amount of manganese found, there was deducted the quantity which was introduced in determining the excess of oxalic acid by potassium permanganate. Summary of Conclusions-- I Potassium permanganate in weakly acid, in neutral, and in alkaline solutions, is reduced by manganese dioxide which has been prepared in the wet way, with evolution of one and one half atoms of oxygen for each molecule of the permanganate. In other words, the permanganate is reduced to manganese dioxide. II This reduction is most rapid in acid and slowest in alkaline solutions. III The rate of reduction is greatly increased by increasing the proportion of manganese dioxide. IV In concentrated solutions of potassium permanganate, the reduction by manganese dioxide is relatively more rapid than in dilute. V Manganese oxide, prepared in the wet way i.e. by the addition of manganese sulphate to a hot solution containing an excess of permanganate, has the composition MnO₂ as regards the ratio of manganese to available oxygen. VI This oxide is unstable. It loses oxygen spontaneously even at ordinary temperatures. VII The oxygen which is thus lost is recovered when the oxide is again treated with an excess of potassium permanganate. VIII It is suggested that a partial explanation of the reduction of potassium permanganate by manganese oxide may be found in the instability of the latter; in other words that the reduction may consist in alternate reduction and reoxidation processes. But when the rapidity of the reduction is taken into account, it seems probable that a reaction analogous to that between permanganic acid and hydrogen superoxide must also take place. Arthur John Hopkins was born September 20, 1864 in Bridgewater, Massachusetts. Receiving his preparation for college in the public schools of that town, he entered Amherst College in 1881 and graduated with the degree of A. B. in 1885. The five years following were spent in teaching in the States of Massachusetts and New York. He entered the Johns Hopkins University in 1890, was assistant in the quantitative laboratory of that university during the academic year of 1891-92, and the following year was appointed Fellow in Chemistry.