These vapors, purified by ebullition at a low temperature, rise into a second rectifying column, G, which terminates in the refrigerator, H, filled with liquid sulphurous anhydride. This refrigerator is like those which we employ in our sulphurous anhydride frigorific apparatus. Under the action of a special pump, M, this liquid produces and maintains a constant temperature of -25° to -30° in the refrigerator. The vapors of alcohol condense therein at this low temperature, and the cold liquid alcohol flows into the lower part of the refrigerator. By the action of a return cock, a portion of this liquid falls upon the plates of the column, G, and descends, while the vapors are rising therein. The other portion of the liquid obtained flows into the reservoir, K, at the beginning of the operation, and into the reservoir, L, during all the remainder of the rectification. The ice-making machine keeps up of itself alone the two operations. In fact, the exhaust of the steam engine which actuates the sulphurous anhydride pump is directed into a worm which circulates through the first boiler, A, and the refrigerator, H, of the frigorific machine keeps up the second rectification, which was brought about below the surrounding temperature, and which for this reason takes place without necessitating any combustion of coal. It suffices to cause the current of water which issues from the condenser of the frigorific machine to pass into the worm of the boiler. We have, then, two results, two like operations, both produced by the working of a single machine. Moreover, these two operations are performed _in vacuo_, and we know that under these conditions they are effected at lower temperatures. Owing to this fact, likewise, the weight of the water that must be evaporated diminishes just so much. Now, one kilogramme of water requires 636 heat units to cause it to pass from the liquid to the gaseous state, while one kilogramme of alcohol requires only 230 heat units to vaporize it. Thus every decrease of temperature in rectification has for an immediate corollary an important economy of fuel, which is proved by the diminution of radiation, and by the less quantity of water to be distilled. Between the boilers, A, in which is maintained a temperature bordering on +50° to +60°, and the refrigerator, H, in which is easily obtained a temperature of -30° to -40°, there is at our disposal a range of temperature of nearly 100°, an immense difference compared with that which can be made use of in ordinary apparatus. Thanks to this powerful factor, which is manageable at will, we can take directly from the apparatus alcohols marking 98 and 99 degrees by the centigrade alcoholmeter. Such results are unobtainable by the usual methods. We have likewise ascertained that at low temperatures the ebullition of alcohol is as active as at near 100°.