In this case, as in the former, the total quantity of steam consumed is that of one cubic inch of water; but the mechanical effect it produces is still further increased. To calculate its amount, we must consider that half a ton of water has fallen through two feet, which is equivalent to a ton falling through one foot, besides which the sixth part of a ton has fallen through one foot. The total loss, therefore, by the fall of water has been one ton and one sixth through one foot, while the force gained by the ascent of water has been one ton raised through three feet, which is equivalent to three tons through one foot. If, then, from three tons we deduct one and one sixth, the remainder will be one ton and five sixths raised through one foot; this effect being above 80 per cent. more than that which is produced in the first case, where the steam was not allowed to expand. To carry the inquiry one step further: Let us suppose that, upon the arrival of the piston at P´´´, a further addition of water to the amount of one twelfth of a ton be added to it: this, with the water it already contained, would make the total contents three fourths of a ton; consequently, the effective pressure upon the piston would now be reduced to one fourth of the atmospheric pressure. The atmospheric steam would balance this when expanded into four times its original volume: consequently, the piston would come to a state of rest at P´´´´, four feet above the bottom of the tube, and the vessel W would consequently have descended through four perpendicular feet. If the steam in the tube be now condensed as in the former cases, and at the same time a quarter of a ton of water be added to the vessel W, the piston will descend to the bottom of the tube, and the ton of water in the vessel W will be raised through four perpendicular feet. To estimate the mechanical effect thus produced, we have, as before, to deduct the total force lost by the fall of water from the force gained by its elevation: the water has fallen in three distinct portions: first, half a ton has fallen through three perpendicular feet, which is equivalent to one ton and a half through one foot; secondly, one sixth of a ton has fallen through two perpendicular feet, which is equivalent to one third of a ton through one foot; and thirdly, one twelfth of a ton has fallen through one foot: these added together will be equivalent to one ton and eleven twelfths through one foot. One ton has been raised through four feet, which is equivalent to four tons through one foot: deducting from this the force lost by the descent, the surplus gained will be two tons and one twelfth through one foot, being about 108 per cent. more than the force resulting from the condensation of steam without expansion.