By continuing this process, water is forced into the air-vessel, and the air which originally filled that vessel is compressed into the space above the water; and its elastic force increases exactly in the same proportion as its bulk is diminished. (6.) Now, suppose that half of the vessel I has been filled by the water which is forced in, the air above the water being reduced to half its bulk has acquired twice the elastic force, and therefore presses on the surface of the water with twice the pressure of the atmosphere. Again, if two thirds of the air-vessel be filled with water, the air is compressed into one third of its bulk, and presses on the surface of the water with three times the pressure of the atmosphere, and so on. [Illustration: Pl. III.] Now if the cock M be opened, the pressure of the condensed air will force the water up in the tube N, and it will continue to rise until the column balances the pressure of the condensed air. If, when the water is suspended in the tube, and the cock M open, the vessel I is half filled, the height of the column in N will be 34 feet, because 34 feet of water has a pressure equal to the atmosphere; and this, added to the atmospheric pressure on it, gives a total pressure equal to twice that of the atmosphere, which balances the pressure of the air in I reduced to half its bulk. If two thirds of I be filled with water, a column of 68 feet will be supported in N; for such a column, united with the atmospheric pressure on it, gives a total pressure equal to three times that of the atmosphere, which balances the air in I compressed into one third of its original bulk. By omitting the principle of condensation, this machine loses 26 feet in the perpendicular lift. But, indeed, in every point of view, it is inferior to the engines of Savery and Newcomen. (45.) From the construction of the atmospheric engine by Newcomen, in 1705, for about half a century, no very important step had been made in the improvement of the steam engine. During this time the celebrated Smeaton had given much attention to the details of the atmospheric engine, and brought that machine to as high a state of perfection as its principle seemed to admit, and as it has ever since reached. In the year 1763, JAMES WATT, a name illustrious in the history of mechanical science, commenced his experiments on steam. He was born at Greenock, in the year 1736; and at the age of 16 was apprenticed to a mathematical instrument-maker, with whom he spent four years. At the age of 20 he removed to London, where he still pursued the same trade under a mathematical instrument-maker in that city. After a short time, however, finding his health declining, he returned to Scotland, and commenced business on his own account at Glasgow. In 1757 he was appointed mathematical instrument-maker to the university of Glasgow, where he resided and carried on business.