Dear reader! It rests with you and me, whether, in our two fields of action, similar things shall be or not. Let them be! We shall sit with lighter bosoms on the hearth, to see the ashes of our fires turn gray and cold.
But hearths seem not to have places for sitting on them, except maybe the narrow shelfs fit for cats and suchlike creatures. I would understand 'sit by the hearth' or 'sit close to the hearth', but why on?
I found some instances of the same use of the on preposition at Google Books, like this one:
I took a couple of snap shots of Judy, who had moved to sit on the hearth to get closer to the warm fire.
She set down the bellows and stood, saying, “Please, sit on the hearth and dry yourself. And can I get you anything? Hot tea . . . or wine?” Finn sat down on the wide stone hearth, and held his hands up to the flames. “No, thank you,” he replied, ...
Could one sit on any hearth or only on a hearth that has a special area extending into the room?
I just can't help recalling James Winterbottom, Esq. when I read "please, sit on the hearth". (0: