Throwing your hat

Does any one know the origin of the saying 'to throw one's hat/cap through the door?

I've seen that action in an old movie and took it as a test to see if the hat-owner is welcome to enter.

There is an old Irish custom of throwing your cap through the door to establish whether you're welcome or not: if not then it's thrown out immediately otherwise it's safe to go in, retrieve it and visit.

Another good reason to wear a hat.

In politics in the US, 'throwing your hat in the ring' is the first overt and public step to becoming a candidate for political office. Like the Irish use, the response to this act determines if there might be a willing electorate to support your candadicy.