Ringling Bros -- The Show Will Go On After Accident ... MINUS Flying Hair-ialists

The Ringling Bros and Barnum & Bailey circus will keep chugging along after a devastating accident Sunday involving its high-flying "Hair Hang" act -- but the ""Hair Hang" act won't be coming along ... a rep for the circus tells TMZ.

The rep tells us, 8 of the 9 acrobats who were injured during the accident -- when a rigging structure failed, dropping the acrobats 30 feet into the center ring -- are still in the hospital ... making it difficult to include the act in upcoming performances in Hartford later this week.

The rep tells us, the girls involved in the accident are the only ones trained to do the act, so the act had to be cut while they recover.

We also spoke to a spokesperson for the circus in D.C., who gave us some interesting trade secrets behind the "Hair Hang" act ... like the fact that the performers weave a metal loop into their hair to help them stay suspended. And there's more where that came from.