On your way south, you take the position from i.e Arcturus to Polaris.
Then from Arcturus to Beltelgeuse
Then from Betelgeuse to another star in the southern hemisphere.
Then from that star to the southern cross.

Retaining the final overall result, you could find the position of Polaris from anypoint far south, couldn't you ? (Errrm!)

I don't know if it's a good method, but it surely was the one my grandgrandgrandgrandgrandgrandfather used when sailing southern seas with his sword and his pirat flag !!!
;-)