Origin and meaning of "Hello the fire!"

I believe this is a variant of "hello the camp", which is used as your father describes: when you're about to enter someone's encampment, as a kind of warning/greeting in lieu of knocking on the nonexistent door. (There's an elided "to" in there: the full/grammatical form would be "hello to the camp".)

I imagine "hello the fire" could be used if there isn't an encampment to speak of, just a fire with guys sitting around it.

This seems to be a quote from 19th century American entertainer Dan Rice. Beyond that I can find nothing as to the source or context of the quote.