Page:Elementary Text-book of Physics (Anthony, 1897).djvu/158

144 The working portion of the air-pump is constructed essentially like the common lifting-pump already described. The valves must be light and accurately fitted. The vessel from which the air is to be exhausted is joined to the pump by a tube, the orifice of which is closed by the valve in the bottom of the cylinder.

A special form of vessel much used in connection with the air-pump is called the receiver. It is usually a glass cylinder, open at one end and closed by a hemispherical portion at the other. The edge of the cylinder at the open end is ground perfectly true, so that all points in it are in the same plane. This ground edge fits upon a plane surface of roughened brass, or ground glass, called the plate, through which enters the tube which joins the receiver to the cylinder of the pump. The joint between the receiver and the plate is made tight by a little oil or vaseline.

The action of the pump is as follows: As the piston is raised, the pressure on the upper surface of the valve in the cylinder is diminished, and the air in the vessel expands in accordance with Boyle's law, lifts the valve, and distributes itself in the cylinder, so that the pressure at all points in the vessel and the cylinder is the same. The piston is now forced down, the lower valve is closed by the increased pressure on its upper surface, the valve in the piston is opened, and the air in the cylinder escapes. At each successive stroke of the pump this process is repeated, until the pressure of the remnant of air left in the vessel is no longer sufficient to lift the valves.

The density of the air left in the vessel after a given number of strokes is determined, provided there be no leakage, by the relations of the volumes of the vessel and the cylinder.

Let $$V$$ represent the volume of the vessel, and $$C$$ that of the cylinder when the piston is raised to the full extent of the stroke. Let $$d$$ and $$d_{1}$$ respectively represent the density of the air in the vessel before and after one stroke has been made. After one down and one up stroke have been made, the air which filled the volume $$V$$ now fills $$V + C$$. It follows that $$\frac{d_{1}}{d} = \frac{V}{V + C}\cdot$$ As this ratio is