In the first case acceleration is imparted to the piston by its own weight and by the pressure of the compressed air in the vessel (since the volume of the cylindrical part is small by comparison with the vessel's volume, we may consider that the air's pressure is constant throughout the period of the piston's motion in the cylinder). But the sphere will not exert pressure on the piston, since it falls only under the force of gravity, i.e, with less acceleration than the piston, from which it is therefore separated.
THE DYNAMICS OF MOTION IN A STRAIGHT LINE 107
The sphere does not therefore alter the piston's acceleration and so does not alter the time during which it moves. In the second case the pressure exerted by the gas is the same, but the piston's mass is greater. So the piston's acceleration will be less, and the time during which the piston moves in the cylinder will be greater than in the first case.