Page:Elementary Text-book of Physics (Anthony, 1897).djvu/159

§ 123] constant no matter what density may be considered, it follows that, if $$d_{n}$$ represent the density after $$n$$ strokes, As this fraction cannot vanish until $$n$$ becomes infinite, it is plain that a perfect vacuum can never, even theoretically, be obtained by means of the air-pump. If, however, the cylinder be large, the fraction decreases rapidly, and a few strokes are sufficient to bring the density to such a point that either the pressure is insufficient to lift the valves, or the leakage through the various joints of the pump counterbalances the effect of longer pumping.

In the best air pumps the valves are made to open automatically. In Fig. 41 is represented one of the methods by which this is accomplished. They can then be made heavier and with a larger surface of contact, so that the leakage is diminished, and the limit of the useful action of the pump is much extended. With the best pumps of this sort a pressure of half a millimetre of mercury is reached.

The Sprengel air-pump depends for its action upon the