I think that Esmeralda I was a sail frigate (built in Spain and captured by Adm. Cochrane), Esmeralda II a steam corvette (skipper Cmdr. A. Prat) and Esmeralda III an Elswick protected cruiser (later sold to Japan during the sino-japanese war). Esmeralda IV was an armoured cruiser, laid down in 1895. Cheers.
In fact all those ships were registered "Esmeralda".
But the last two ones were BOTH "Elswick Cruiser", The second being almost an improvement (with a very narrow armoured belt) of the first.
So most of the time Esmeralda II refer to this ship. Personnally if i was talking about the several Chilean ships that were called Esmeralda i would say first Esmeralda, second Esmeralda, third Esmeralda .........and so on.