I strongly recommend your acqusition of Frank Grahams book. The volume one uses the Bilgram diagram with an explanation that any mechanic/machinist can understand (that's what the name is about - it was meant to be carried in the hip pocket. There are several other errors/misconceptions that...
The two slide valves ride one atop the other; one is for direction control (ahead-astern) and the other regulates cutoff. In Audels Engineers and Mechanics Guide, Vol. I, there is an explanation of this type of valve as well as a very detailed description of the valve gear and its control...