The correct answer is B) Movement of the main piston through the steam cylinder. The position of the pilot slide valve in a reciprocating pump is controlled by the movement of the main piston through the steam cylinder. As the main piston moves, it actuates the pilot slide valve, which in turn controls the admission and exhaust of steam to and from the pump's steam cylinder. This mechanism allows the pump to operate automatically and adjust the stroke of the main piston based on the system's demand. The other answer choices are incorrect because they do not directly control the pilot slide valve's position. Moving tappets, adjusting tappet collars, and stay rods are all related to the pump's mechanical components, but they do not specifically govern the pilot slide valve's movement.