That is a spring loaded tuning slide similar to what Reynolds and Conn used on their 4-valve euphoniums (Contempora for Reynolds and Connstellation for Conn). Conn shipped the Connstellation for a number of years (late 50's until early 70's). Reynolds only made a few 4-valve Contempora's with the adjustable tuning slide. A tuning slide trigger is now 'de-riguer" on high end compensating euphoniums like Besson Prestige, Sterling, and York Emminence.
A true compensating system involves a complete extra set of loops that are engaged when the 3rd valve is used (for 3 valve horns) or the 4th valve is used (for 3+1 horns).