Parts of a brass instruments?

Mouthpiece is correct. The valves send the air into longer lengths of pipe that branch off of them. The parts that move in and out of the valves are valve slides. The parts that slide and are not connected to the valves are tuning slides most often. The large part where the sound comes out is the bell, or the bell flair, the gradual enlarging part that is connected to the bell is the bell throat. The design of all the enlarging parts are known as the "horn's tapers". The part where the mouthpiece plugs into is known as the leadpipe. Each part is numbered by its relationship to the bell. The first pipe that is connected to the bell is the "first branch" the part that connects to that is the "second branch" (I am on a roll here). The valves are numbered by their closeness to the player's lips, the first valve being the closest. Feel free to email me with other Qs.