Experiments with low concentrations of sugar are difficult to interpret, the influence of the hydrolysis of glycogen and of dextrins on the one hand, and the synthesis of sugar to more complex carbohydrates on the other (p. 31), having a relatively great effect on the concentration of the sugar. Unpublished experiments (Harden and Young) indicate, however, that the velocity of fermentation remains approximately constant, until a certain very low limit of sugar concentration is reached, and then falls rapidly. The fall in rate, however, only continues over a small interval of concentration, after which the velocity again becomes approximately constant and equal to the rate of autofermentation. During this last phase, as already indicated, the velocity is generally controlled by the rate of production of sugar and no longer by that of phosphate, this substance being now present in excess. In other words, the rate of fermentation of sugar by yeast-juice and zymin is not proportional to the concentration of the sugar present as required by the law of mass, but, after a certain low limit of sugar concentration, is independent of this and is actually slightly decreased by increase in the concentration of the sugar. The relations here are very similar to those shown to exist by Duclaux [1899] and Adrian Brown [1902] for the action of invertase on cane sugar and are probably to be explained in the manner suggested by the latter. According to this investigator, the enzyme unites with the fermentable material, or as it is now termed, the substrate or zymolyte, forming a compound which only slowly decomposes so that it remains in existence for a perceptible interval of time. The rate of fermentation depends on the rate of decomposition of this compound and hence varies with its concentration. This conception leads to the result that the rate of fermentation will increase with the concentration of the substrate up to a certain limit and will then remain [p122] constant, unless interfered with by secondary actions. This limit of concentration is that at which there is just sufficient of the material in question present to combine with practically the whole of the enzyme, so that no further increase in its amount can cause a corresponding increase in the quantity of its compound with the enzyme or in the rate of fermentation which depends on the concentration of that compound. The curve relating the rate of action of such an enzyme with the concentration of the zymolyte therefore consists of two portions, one in which the rate at any moment is proportional to the concentration of the zymolyte, according to the well-known law of the action of mass, and a second in which the rate at any moment is almost independent of that concentration, approximately equal amounts being decomposed in equal times whatever the concentration of the substrate.