'One of the earliest recorded references to drumming out occurs in Alexander Pope's Moral Essays, 3rd epistle, 1731–1733: "Chartres was a man infamous for all manner of vices. When he was an ensign in the army, he was drummed out of the regiment for a cheat; he was next banished Brussels, and drummed out of Ghent, on the same account'
'Cashiering (or degradation ceremony), generally within military forces, is a ritual dismissal of an individual from some position of responsibility for a breach of discipline'
Thank you for your answers. I never thought of it in a military sense. I was trying to think of cashiering out in a monetary sense. I have learnt something new tonight!