Supposing, then, the total force exerted upon the piston, after deducting the resistance from the uncondensed vapour, to be one ton, and the length of the cylinder to be one foot, each motion of the piston from end to end of the cylinder will produce a mechanical force equivalent to a ton weight raised one foot high. If in this case the magnitude of the piston be equivalent to one square foot, the pressure of the steam will be equal to that of the atmosphere, and the quantity of water in the form of steam which the cylinder will contain will be a cubic inch, while the quantity of steam in it will be a cubic foot. In proportion as the area of the piston is enlarged the pressure of the steam will be diminished, if the moving force is required to remain the same; but with every diminution of pressure the density of the steam will be diminished in the same proportion, and the cylinder will still contain the same quantity of water in the form of vapour. In this way steam may be used, as a mechanical agent, with a pressure to almost any extent less than that of the atmosphere, and at temperatures considerably lower than 212°. To obtain the same mechanical force, it is only necessary to enlarge the piston in the same proportion as the pressure of the steam is diminished. By a due attention to this circumstance, the expansive power of steam, both in its direct action and by condensation, may be used with very much increased advantage; and such is the principle on which the benefits derived from Woolf's contrivances depend. If steam of a high-pressure, say of three or four atmospheres, be admitted to the piston, and allowed to impel it through a very small portion of the descent, it may then be cut off and its expansion may be allowed to act upon the piston until the pressure of the steam is diminished considerably below the atmospheric pressure; the steam may then be condensed and a vacuum produced, and the process repeated. In the double-acting engines, commonly used in manufactures and in navigation, and still more in the high-pressure engines used for locomotion, the advantageous application of the principle of expansion appears to have been hitherto attended with difficulties; for, notwithstanding the benefits which unquestionably attend it in the economy of fuel, it has not been generally resorted to. To derive from this principle full advantage, it would be necessary that the varying power of the expanding steam should encounter a corresponding, or a nearly corresponding, variation in the resistance: this requisite may be attained, in engines applied to the purpose of raising water, by many obvious expedients; but when they have, as in manufactures, to encounter a nearly uniform resistance, or, in navigation and locomotion, a very irregular resistance, the due application of expansion is difficult, if indeed it be practicable.