Elaborate on the intricate operational sequence and internal mechanism of a distributing valve during a service brake application in a conventional locomotive pneumatic braking system.

A conventional locomotive pneumatic braking system utilizes a distributing valve as a central component to manage brake cylinder pressure independently of brake pipe variations and to ensure brake cylinder pressure is maintained against leakage. During a service brake application, the process begins from a fully charged state, where the brake pipe and the auxiliary reservoir on the locomotive are charged to the same pressure, and the locomotive’s brake cylinders are exhausted to the atmosphere. When the locomotive engineer initiates a service brake application, they make a controlled reduction in brake pipe pressure using the automatic brake valve. This reduction creates a pressure differential across the equalizing piston within the distributing valve. The auxiliary reservoir, which remains at its higher initial pressure, now exerts a greater force on one side of the equalizing piston than the reduced brake pipe pressure on the other side. This pressure difference causes the equalizing piston to move. As the equalizing piston begins its movement, it first moves the graduating valve off its seat. Further movement of the equalizing piston then pulls the main slide valve along with it. The movement of the main slide valve aligns specific ports within the distributing valve. This alignment connects the auxiliary reservoir to the application chamber, which is a small, fixed-volume chamber within the distributing valve. Air from the auxiliary reservoir flows into and charges the application chamber. The pressure established in the application chamber becomes the control pressure that dictates the target brake cylinder pressure for the locomotive’s brakes. This application chamber pressure then acts upon one side of the application piston. On the opposite side of the application piston, brake cylinder pressure and atmospheric pressure are present. The higher application chamber pressure forces the application piston to move. This movement of the application piston simultaneously closes the exhaust valve, preventing any air from escaping the brake cylinders, and opens the application valve. With the application valve open, air from the locomotive’s main reservoir, which is maintained at a high pressure by the air compressor, is allowed to flow directly into the locomotive’s brake cylinders. As main reservoir air enters the brake cylinders, their pressure increases, causing the brake shoes to apply against the wheels. As brake cylinder pressure builds, it also acts upon the side of the application piston opposite the application chamber. When the brake cylinder pressure builds sufficiently to create a force on the application piston that is equal to the force exerted by the application chamber pressure, the application piston moves back slightly. This small reverse movement causes the application valve to close, cutting off the flow of main reservoir air to the brake cylinders, and simultaneously seats the exhaust valve, preventing any brake cylinder air from escaping. This specific position is known as the lap position. In the lap position, no air is entering or leaving the brake cylinders, and the pressure within them is maintained precisely at the level commanded by the application chamber. The critical function of the distributing valve in this lap position is to continuously monitor the brake cylinder pressure. If any leakage occurs from the brake cylinders, causing their pressure to drop, the application chamber pressure will again become comparatively higher than the brake cylinder pressure. This pressure differential will cause the application piston to move slightly again, re-opening the application valve just enough to admit more main reservoir air into the brake cylinders until the pressure is restored to the predetermined level set by the application chamber, ensuring that the brake force remains constant despite leakage.