Again, let the load placed upon the piston be five tons: the evaporation of the water will raise this through the sixth part of a foot; if one ton be now removed, the other four tons will be raised to a height above the bottom of the tube equal to a fifth part of a foot; another ton being removed, the remaining three will be raised to a height from the bottom equal to a fourth of a foot; and so on, the last ton being raised through half a foot. To estimate the total mechanical effect thus produced, we are to consider that the several tons raised from their first position are raised through the sixth, fifth, fourth, third, and half of a perpendicular foot, giving a total effect equal to the sixth, fifth, fourth, third, and half of a ton severally raised through one foot; these, therefore, added together, will give a total of nineteen twentieths of a ton raised through one foot.

In general, the expansive force applied to the direct action of high-pressure steam, therefore, will increase its effect according to the same law, and subject to the same principles as were shown with respect to the method of condensation accompanied with expansion.

The expansive action of high-pressure steam may be accompanied with condensation, so as considerably to increase the mechanical effect produced; for, after the weights with which the piston is loaded have been successively raised to the extent permitted by the elastic force of the steam, and are removed from the piston, the steam will expand until it balances the atmospheric pressure. It may afterwards be made further to expand, by adding weights to the counterpoise W in the manner already explained; and, the steam being subsequently condensed, all the effects will be produced upon the descent of the piston which we have before noticed. It is evident that by this means the mechanical effect admits of very considerable increase.

(135.) We have hitherto considered the piston to be resisted by the atmospheric pressure above it; but, as is shown in the preceding chapters, in the modern steam engines, the atmosphere is expelled from the interior of the machine by allowing the steam to pass freely through all its cavities in the first instance, and to escape at some convenient aperture, which, opening outwards, will effectually prevent the subsequent re-admission of air. The piston-rod and other parts which pass from the external atmosphere to the interior of the machine, are likewise so constructed and so supplied with oil or other lubricating matter that neither the escape of steam nor the entrance of air is permitted. We are therefore now to consider the effect of the action of steam against the piston P, when subjected to a resistance which may be less in amount, to any extent, than the atmospheric pressure.

In such machines the steam always acts both directly by its power, and indirectly by its condensation. In calculating its effects, excluding friction, &c., we have therefore only to estimate its total force upon the piston, and to deduct the force of the uncondensed vapour which will resist the motion of the piston.

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.

We have seen that the mechanical effect produced by steam when the principle of expansion is not used, is always proportional to the quantity of water contained in the steam, and is likewise in the same proportion so long as a given degree of expansion is used. It is apparent, therefore, that the mechanical power which is or ought to be exerted by an engine is in the direct proportion of the quantity of water evaporated. It has also been shown that the quantity of water evaporated, whatever be the pressure of the steam, will be in the direct proportion of the quantity of heat received from the fuel, and therefore in the direct proportion of the quantity of fuel itself, so long as the same proportion of its heat is imparted to the water.

(136.) The POWER of an engine is a term which has been used to express the rate at which it is able to raise a given load, or overcome a given resistance. The DUTY of an engine is another term, which has been adopted to express the load which may be raised a given perpendicular height, by the combustion of a given quantity of fuel.