Mechanical efficacy of steam -- proportional to the quantity of water evaporated, and to the fuel consumed -- Independent of the pressure. -- Its mechanical efficacy by condensation alone. -- By condensation and expansion combined -- by direct pressure and expansion -- by direct pressure and condensation -- by direct pressure, condensation, and expansion. -- The power of engines. -- The duty of engines. -- Meaning of horse power. -- To compute the power of an engine. -- Of the power of boilers. -- The structure of the grate-bars. -- Quantity of water and steam room. -- Fire surface and flue surface. -- Dimensions of steam pipes. -- Velocity of piston. -- Economy of fuel. -- Cornish duty reports. (130.) Having explained in the preceding chapters the most important circumstances connected with the principal varieties of steam engines, it remains now to explain some matters of detail connected with the power, efficiency, and economy of these machines, which, though perhaps less striking and attractive than the subjects which have hitherto engaged us, are still not undeserving of attention. It has been shown in the first chapter, that water exposed to the ordinary atmospheric pressure (the amount of which may be expressed by a column of 30 inches of mercury) will pass from the liquid into the vaporous state when it arrives at the temperature of 212°; and the vapour thus produced from it will have an elastic force equal to that of the atmosphere. If the water, however, to which heat is applied, be submitted to a greater or less pressure than that of the atmosphere, it will boil at a greater or less temperature, and will always produce steam of an elastic force equal to the pressure under which it boils. Now it is a fact as remarkable as it is important, that to convert a given weight of water into vapour will require the same quantity of heat, under whatever pressure, and at whatever temperature the water may boil. Let us suppose a tube, the base of which is equal to a square foot, in which a piston fits air-tight and steam-tight. Immediately under the piston, let a cubic inch of water be placed, which will be spread in a thin layer over the bottom of the tube. Let the piston be counterbalanced by a weight (acting over a pulley) which will be equivalent to the weight of the piston, so that it shall be free to ascend by the application of any pressure below it. Now let the flame of a lamp be applied at the bottom of the tube: the water under the piston being affected by no pressure from above, except that of the atmosphere acting upon the piston, will boil at the temperature of 212°, and by the continued application of the lamp it will at length be converted into steam. The steam into which the cubic inch of water is converted will expand into the magnitude of a cubic foot, exerting an elastic force equal to the atmospheric pressure;