In this arrangement the pistons ascend and descend together, and their rods must consequently be attached to the beam at the same side of the centre. It is sometimes desirable that they should act on different sides of the centre of the beam, and consequently that one should ascend while the other descends. It is easy to arrange the valves so as to effect this. In fig. 45., the lesser piston is at the bottom of the cylinder, and the greater at the top. On opening the valves C´, E´, F´, a vacuum is produced below the greater piston, and steam flows from the lesser cylinder, through E´, _above_ the greater piston, and presses it down. At the same time steam being admitted from the boiler through C´ below the lesser piston, forces it up against the diminishing force of the steam above it, which expands into the greater cylinder. Thus as the greater piston descends the lesser ascends. When each has traversed its cylinder, the valves C´, E´, F´ being closed, and C, E, F opened, the lesser piston will descend, and the greater ascend, and so on. (78.) The law according to which the elastic force of steam diminishes as it expands, of which Mr. Woolf appears to have been entirely ignorant, is precisely similar to the same property in air and other elastic fluids. If steam expands into twice or thrice its volume, it will lose its elastic force in precisely the same proportion as it enlarges its bulk; and therefore will have only a half or a third of its former pressure, supposing that as it expands its temperature is kept up. Although Mr. Woolf's patent contained the erroneous principle which we have noticed, yet, so far as his invention suggested the idea of employing steam at a very high-pressure, and allowing it to expand in a much greater degree than was contemplated either by Watt or Hornblower, it became the means of effecting a considerable saving in fuel; for engines used for pumping on a large scale, the steam being produced under a pressure of forty or fifty pounds or more upon the square inch, might be worked first through a small space with intense force, and the communication with the boiler being then cut off, it might be allowed, with great advantage, to expand through a very large space. Some double-cylinder engines upon this principle have been worked in Cornwall, with considerable economy. But the form in which the expansive principle, combined with high pressure, is now applied in the engines used for raising water from the mines, is that in which it was originally proposed by Watt. A single cylinder of considerable length is employed; the piston is driven through a small proportion of this length by steam, admitted from the boiler at a very intense pressure: the steam being then cut off, the piston is urged by the expansive force of the steam which has been admitted, and is by that means brought to the bottom of the cylinder.