It results from all the laws that we have cited that by properly regulating the tensions of the vapors of a mixture of alcohol and water, and the temperature of the liquid, we shall be able to obtain a liquid of a desired richness by the condensation of these vapors. III. It was likewise indispensable to make sure of one important fact: When the temperature of a liquid like alcohol is considerably lowered, can the distillation of a given weight of this substance be effected with sufficient rapidity for industrial requirements? Repeated experiments with a host of volatile liquids have demonstrated the following laws: If we introduce a volatile liquid into two spherical receivers connected by a wide tube, and if these be kept at different temperatures after driving out all the air from the apparatus, the liquid distills from the warmer into the cooler receiver, and we ascertain that: h. The weight of the liquid which distills in the unit of time increases with the deviation of temperature between the two receivers. i. The weight of the liquid which distills in the unit of time is constant for a same deviation of temperature between the receivers, whatever be, moreover, the absolute temperature of the receivers. k. The weight of the liquid distilled in the unit of time is proportional to the active surfaces of the receivers; that is to say, to the surfaces which are the seat of passage of heat through their thickness. l. The least trace of a foreign gas in the vapors left in the apparatus throws the preceding laws into confusion, and checks distillation to a considerable degree, especially at low temperatures. Thus, water distilling between 100° and 60° will pass over as quickly as that which is distilling between 40° and 0°. Absolute temperature is without influence, provided every trace of air or foreign gas be got rid of. The distillatory apparatus should be provided with an excellent air-pump, capable of preventing all those entrances of air which are inevitable in practice. The following is the industrial application that we have endeavored to make of these theoretical views: The rectification of alcohols is one of the most complex of operations; it looks toward several results simultaneously. Alcohol derived from the fermentation of grain, sugar, and of all starchy matters in general, contains an innumerable host of different products, which may be grouped under four principal heads: 1. Empyreumatic essential oils, characteristic of the source of the alcohol, and having a powerful odor which infects the total mass of the crude spirits. 2. A considerable quantity of water. 3. A certain quantity of pure alcohol. 4. A variable proportion of volatile substances, composed in great part of ethers, different alcohols, and bodies as yet not well defined. These latter affect the quality of the alcohol by an odor which is entirely different from that of the essential oils.