They control the admission of steam into the cylinders and its subsequent exhausting, enabling a locomotive to move under its own power.
The valve consists of two piston heads on a common spindle moving inside a steam chest, which is essentially a mini-cylinder located either above or below the main cylinders of the locomotive.
[3] This entails controlling the admission and exhaust of steam to and from the cylinders with a valve linked to the motion of the piston.
[3] This is because it allows the steam to remain in the cylinder for the longest possible amount of time before being expended as exhaust, therefore increasing efficiency.
[3] The cylinder on both sides of the piston is open to exhaust at the same time when the valve is passing through the mid-position, which is only momentary when running.
[3] Lead is the amount by which a port is open when the piston is at front or back "dead centre".
The easy approximation (used in Zeuner's and Realeaux's diagrams) is to pretend that both the valve and the piston have a sine-wave motion (as they would, if the main rod were infinitely long).