We have current flowing across the mercury (from one ring to the other), which is sitting in a magnetic field. So there is a F=BIL magnetic force. Or we can think the moving electrons (that constitute the current) experience a F=Bqv magnetic force. This force is directed perpendicular to the current (and magnetic field), which turns out to be along the circumference of the ring. The mercuy is thus pumped in a merry-go-round fashion.
Why should the metal lattice chase after/get dragged by the electrons?