Bailum and Barney's Great Consolidated Shows is an American circus featuring three rings in one tent and a menagerie on the side. Oscar Z. Diggs, aka the Great Oz, worked for the circus as a balloonist, going up in a hot-air balloon to attract crowds. (The Wonderful Wizard of Oz, Dorothy and the Wizard in Oz)
Background[]
This is likely a reference to the real life "Barnum & Bailey's Greatest Show on Earth", which was founded in 1881 and well known when the early Oz books were written. The circus eventually became the "Ringling Bros. and Barnum & Bailey Circus" and ran for 146 years. [1]
"Prequels" to the original Wizard of Oz story sometimes show Diggs performing in the circus. In Donald Abbott's novel How the Wizard Came to Oz (1991), the circus is unnamed. In the 2013 film Oz the Great and Powerful, it is called Baum Brothers Circus.