To remove these difficulties, a pump is placed near the condenser communicating with it by a valve M, which opens from the condenser into the pump. In this pump is placed a piston which moves air-tight, and in which there is a valve N, which opens upwards. Now suppose the piston at the bottom of the pump. As it rises, since the valve in it opens _upwards_, no air can pass _down_ through it, and consequently it leaves a vacuum _below_ it. The water and any air which may be collected in the condenser open the valve M, and pass into the lower part of the pump from which they cannot return in consequence of the valve M opening _outwards_. On the descent of the pump-piston, the fluids which occupy the lower part of the pump, force open the piston-valve N; and passing through it, get _above_ the piston, from which their return is prevented by the valve N. In the next ascent, the piston lifts these fluids to the top of the pump, whence they are discharged through a conduit into a small cistern B by a valve K which opens outwards. The water which is thus collected in B is heated by the condensed steam, and is reserved in B, which is called the hot well for feeding the boiler, which is effected by means which we shall presently explain. The pump which draws off the hot water and air from the condenser is called the _air-pump_. (50.) We have not yet explained the manner in which the valves and the air-pump piston are worked. The rod Q of the latter is connected with the working beam, and the pump is therefore wrought by the engine itself. It is not very material to which arm of the beam it is attached. If it be on the same side of the centre of the beam with the cylinder, it rises and falls with the steam-piston; but if it be on the opposite side, the pump-piston rises when the steam-piston falls, and _vice versâ_. In the single-engine there are some advantages in the latter arrangement. As the steam-piston _descends_, the steam rushes into the condenser, and the jet is playing; and this, therefore, is the most favourable time for drawing out the water and condensed steam from the condenser by the ascent of the pump-piston, since by this means the descent of the steam-piston is assisted; an effect which would not be produced if the steam-piston and pump-piston descended together. With respect to the method of opening and closing the valves, it is evident that the three valves which are simultaneously opened and closed may be so connected as to be worked by the same lever. This lever may be struck by a pin fixed upon the rod Q of the air-pump, so that when the pistons have arrived at the top of the cylinders the pin strikes the lever and opens the three valves. A catch or detent is provided for keeping them open during the descent of the piston, from which they are disengaged in a similar manner on the arrival of the piston at the bottom of the cylinder, and they close by their own weight.